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Artykuły w czasopismach na temat „Semi-Riemannian manifold”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Gündüzalp, Yılmaz. "Anti-Invariant Semi-Riemannian Submersions from Almost Para-Hermitian Manifolds." Journal of Function Spaces and Applications 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/720623.

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We introduce anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds onto semi-Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a semi-Riemannian submersion, and check the harmonicity of such submersions. We also obtain curvature relations between the base manifold and the total manifold.

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2

Sari, Ramazan, та Mehmet Akyol. "Hemi-slant ξ⊥-Riemannian submersions in contact geometry". Filomat 34, № 11 (2020): 3747–58. http://dx.doi.org/10.2298/fil2011747s.

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M. A. Akyol and R. Sar? [On semi-slant ??-Riemannian submersions, Mediterr. J. Math. 14(6) (2017) 234.] defined semi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. As a generalization of the above notion and natural generalization of anti-invariant ??-Riemannian submersions, semi-invariant ??-Riemannian submersions and slant submersions, we study hemi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We obtain the geometry of foliations, give some examples and find necessary and sufficient condition for the base manifold to b

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3

Perrone, Domenico. "Curvature of K-contact Semi-Riemannian Manifolds." Canadian Mathematical Bulletin 57, no. 2 (2014): 401–12. http://dx.doi.org/10.4153/cmb-2013-016-7.

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Abstract.In this paper we characterize K-contact semi-Riemannian manifolds and Sasakian semi- Riemannian manifolds in terms of curvature. Moreover, we show that any conformally flat K-contact semi-Riemannian manifold is Sasakian and of constant sectional curvature κ = ɛ, where ɛ = ± denotes the causal character of the Reeb vector field. Finally, we give some results about the curvature of a K-contact Lorentzian manifold.

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4

Ṣahin, Bayram. "Semi-invariant Submersions from Almost Hermitian Manifolds." Canadian Mathematical Bulletin 56, no. 1 (2013): 173–83. http://dx.doi.org/10.4153/cmb-2011-144-8.

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AbstractWe introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semiinvariant submersions with totally umbilical fibers and show that such submersions put some restrictions on tot

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5

Atçeken, Mehmet. "Warped Product Semi-Invariant Submanifolds in Almost Paracontact Riemannian Manifolds." Mathematical Problems in Engineering 2009 (2009): 1–16. http://dx.doi.org/10.1155/2009/621625.

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We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form by reversing two factor manifolds and . We prove several fundamental properties of warped product semi-invariant submanifolds in an almost paracontact Riemannian manifold and establish a general inequality for an arbitrary warped product semi-invariant subma

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6

Kumar, Tejinder, Sangeet Kumar, and Pankaj Kumar. "Slant Lightlike Submanifolds of Semi-Riemannian Product Manifolds." Sarajevo Journal of Mathematics 19, no. 2 (2024): 155–70. http://dx.doi.org/10.5644/sjm.19.02.02.

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The aim of the present paper is to investigate geometric characteristics of slant lightlike submanifolds of semi-Riemannian product manifolds. We obtain characterization theorems for the existence of slant lightlike submanifolds of semi-Riemannian product manifolds. We also find a necessary and sufficient condition enabling the induced connection on slant lightlike submanifolds of semi-Riemannian product manifolds to be a metric connection. Then, we establish some results for the integrability of distributions associated with this class of lightlike submanifolds. Consequently, we investigate t

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7

Kumar, Sushil, Rajendra Prasad, Abdul Haseeb, and Punit Kumar Sıngh. "A note on pointwise quasi hemi-slant submersions." Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74, no. 2 (2025): 200–209. https://doi.org/10.31801/cfsuasmas.1545937.

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As a generalization of hemi-slant and semi-slant submersions, we discuss pointwise quasi Hemi-slant (PQHS) submersions from almost Hermitian manifolds onto Riemannian manifolds. We obtain various results satisfied by these submersions from Kähler manifolds onto Riemannian manifolds. Moreover, we find necessary and sufficient conditions on integrability of the distributions, and explore the geometry of totally geodesic foliations of discussed submersions. At last, we construct some examples of a PQHS submersion from an almost Hermitian manifold onto a Riemannian manifold.

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8

Sahin, Bayram. "Warped product semi-slant submanifolds of a locally product Riemannian manifold." Studia Scientiarum Mathematicarum Hungarica 46, no. 2 (2009): 169–84. http://dx.doi.org/10.1556/sscmath.46.2009.2.1086.

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In [20], it was shown that there are no warped product semi-slant submanifolds of Kaehler manifolds. In this paper, we show that there exists a class of non-trivial warped product semi-slant submanifolds of a locally product Riemannian manifold contrary to Kaehlerian case. Then, we give a characterization, an example and investigate the geometry of warped product semi-slant submanifolds in a locally product Riemannian manifold.

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9

Erdoğan, Feyza Esra, Selcen Yüksel Perktaş, Şerife Nur Bozdağ, and Bilal Eftal Acet. "Lightlike Hypersurfaces of Meta-Golden Semi-Riemannian Manifolds." Mathematics 11, no. 23 (2023): 4798. http://dx.doi.org/10.3390/math11234798.

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In this research, we embark on the examination of lightlike hypersurfaces within an almost meta-Golden semi-Riemannian manifold. We investigate the properties of the induced structure on a lightlike hypersurface by meta-Golden semi-Riemannian structure. Then, we introduce invariant lightlike hypersurfaces, anti-invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces of almost meta-Golden semi-Riemannian manifolds and give examples.

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10

Longwap, Silas, Shamtang B. Musa, Gukat G. Bitrus, and Ezekiel B. Yohanna. "Local Orthonormal Basis of the Fibres of Quasi-Hemi-Slant Riemannian Submersion." Journal of Advances in Mathematics and Computer Science 38, no. 12 (2023): 1–11. http://dx.doi.org/10.9734/jamcs/2023/v38i121852.

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In this paper we recall some different Riemannian Submersions such as; Semi-Invarian, Semi-Slant, Hemi-Slant and Quasi-Hemi-Slant Submersion from Almost Hermitian manifold to Riemannian manifold. Our goal in this work is to introduce local orthonormal bases for the fibers of Quasi-Hemi-Slant Riemannian submersion which generalizes Hemi-Slant, Semi-Slant and Semi-Invarian submersion from Almost Hermitian manifold to Riemannian manifold.

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11

POYRAZ, NERGIZ (ÖNEN), EROL YAŞAR, and DOĞAN DÖNMEZ. "Half Lightlike Submanifolds of A Golden Semi-Riemannian Manifold." Kragujevac Journal of Mathematics 48, no. 1 (2024): 99–122. http://dx.doi.org/10.46793/kgjmat2401.099p.

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We present half lightlike submanifolds of a golden semi-Riemannian manifold. We prove that there is no radical anti-invariant half lightlike submanifold of a golden semi-Riemannian manifold. We get results for screen semi-invariant half lightlike submanifolds of a golden semi-Riemannian manifold. We prove the conditions for integrability of distributions on screen semi-invariant half lightlike submanifolds and investigate the geometry of leaves of distributions. Moreover, we study screen conformal half lightlike submanifolds of a golden semi-Riemannian manifold.

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12

Gök, Mustafa, and Erol Kılıç. "Totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds." Filomat 36, no. 8 (2022): 2675–86. http://dx.doi.org/10.2298/fil2208675g.

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In this paper, we obtain some classification theorems for totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no totally umbilical proper semi-invariant submanifolds in a posivitely or negatively curved locally decomposable metallic Riemannian manifold

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13

Kaushal, Rupali, Rashmi Sachdeva, Rakesh Kumar, and Rakesh Kumar Nagaich. "Semi-invariant Riemannian submersions from nearly Kaehler manifolds." International Journal of Geometric Methods in Modern Physics 17, no. 07 (2020): 2050100. http://dx.doi.org/10.1142/s0219887820501005.

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We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invar

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14

Stoica, Ovidiu Cristinel. "The geometry of warped product singularities." International Journal of Geometric Methods in Modern Physics 14, no. 02 (2017): 1750024. http://dx.doi.org/10.1142/s0219887817500244.

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In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian man

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15

AYDIN, GÜLŞAH, and A. CEYLAN ÇÖKEN. "SLANT SUBMANIFOLDS OF SEMI-RIEMANNIAN MANIFOLDS." International Journal of Geometric Methods in Modern Physics 10, no. 10 (2013): 1350058. http://dx.doi.org/10.1142/s0219887813500588.

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In this study, we search slant submanifolds of almost product semi-Riemannian manifold. Accordingly, we investigate slant submanifolds of semi-Riemannian manifold by making the classifications as slant Riemannian, slant semi-Riemannian and slant lightlike submanifold. Moreover, we add the theorems which characterize existence of slant submanifold.

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16

Peyghan, E., A. Tayebi, and L. Nourmohammadi Far. "On Twisted Products Finsler Manifolds." ISRN Geometry 2013 (July 10, 2013): 1–12. http://dx.doi.org/10.1155/2013/732432.

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On the product of two Finsler manifolds , we consider the twisted metric which is constructed by using Finsler metrics and on the manifolds and , respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study C-reducible and semi-C-reducible properties of this manifold. Then we obtain the Riemannian curvature and some of non-Riemannian curvatures of the twisted product Finsler manifold such as Berwald curvature, mean Berwald curvature, and we find the relations between these objects and their corresponding objects on and . Finally, we study local

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17

Qayyoom, Mohammad Aamir, Rawan Bossly, and Mobin Ahmad. "On CR-lightlike submanifolds in a golden semi-Riemannian manifold." AIMS Mathematics 9, no. 5 (2024): 13043–57. http://dx.doi.org/10.3934/math.2024636.

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<abstract><p>CR-lightlike submanifolds of a golden semi-Riemannian manifold are the focus of the research presented in this work, which aims to define and investigate these structures. Under the context of a golden semi-Riemannian manifold, we study the properties of geodesic CR-lightlike submanifolds as well as umbilical CR-lightlike submanifolds. In addition, on a golden semi-Riemannian manifold, we find numerous intriguing findings for entirely geodesic and totally umbilical CR-lightlike subamnifolds. Also, we construct an example of a CR-lightlike submanifold of a golden semi-R

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18

Hretcanu, Cristina E., and Adara M. Blaga. "Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor." Mathematics 9, no. 17 (2021): 2125. http://dx.doi.org/10.3390/math9172125.

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In the present paper, we study some properties of warped product pointwise semi-slant and hemi-slant submanifolds in Golden Riemannian manifolds, and we construct examples in Euclidean spaces. Additionally, we study some properties of proper warped product pointwise semi-slant (and, respectively, hemi-slant) submanifolds in a locally Golden Riemannian manifold.

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19

Şahin, Fulya, and Bayram Şahin. "Certain lie algebraic structures on Riemannian manifolds with semi-symmetric non-metric connection." Filomat 37, no. 14 (2023): 4715–23. http://dx.doi.org/10.2298/fil2314715s.

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As a natural consequence of the Levi-Civita connection on a Riemannian manifold, there is a Lie algebra structure on a Riemannian manifold. Lie Algebras and Lie Groups are the mathematical structure of continuous symmetries in physics. In this paper, semi-symmetric non-metric connection is considered instead of Levi-Civita connection of Riemann manifold, and accordingly the existence of algebraic structures is investigated. First, it is shown that there is not always a Lie algebra structure on a Riemannian manifold with a semi-symmetric non-metric connection. Then, necessary and sufficient con

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20

Fatima, Tanveer, and Shahid Ali. "Generic riemannian submersions." Tamkang Journal of Mathematics 44, no. 4 (2013): 395–409. http://dx.doi.org/10.5556/j.tkjm.44.2013.1211.

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B. Sahin [12] introduced the notion of semi-invariant Riemannian submersions as a generalization of anti-invariant Riemmanian submersions [11]. As a generalization to semi-invariant Riemannian submersions we introduce the notion of generic submersion from an almost Hermitian manifold onto a Riemannian manifold and investigate the geometry of foliations which arise from the definition of a generic Riemannian submersion and find necessary and sufficient condition for total manifold to be a generic product manifold. We also find necessary and sufficient conditions for a generic submersion to be t

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21

SAHIN, BAYRAM. "SCREEN CONFORMAL SUBMERSIONS BETWEEN LIGHTLIKE MANIFOLDS AND SEMI-RIEMANNIAN MANIFOLDS AND THEIR HARMONICITY." International Journal of Geometric Methods in Modern Physics 04, no. 06 (2007): 987–1003. http://dx.doi.org/10.1142/s0219887807002405.

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In this paper, we introduce a new submersion ϕ : M → N, namely screen conformal submersion, between a lightlike manifold M and a semi-Riemann manifold N. We give examples and show that the lightlike manifold M is shear free under a condition if ϕ : M → N is a screen conformal submersion. Also we define special screen submersions: radical and screen homothetic submersions. We obtain that the radical homothetic submersion ϕ : M → N implies that M is a Reinhart lightlike manifold. Moreover we define and study the lightlike versions of O'Neill's tensors for a horizontally conformal submersion and

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22

POLAT, Murat. "Clairaut semi invariant submersions from locally product Riemannian manifolds." Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 16, no. 2 (2023): 311–26. http://dx.doi.org/10.18185/erzifbed.1178718.

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The goal of the present paper is to analyze some geometric features of Clairaut semi invariant Riemannian submersions whose total manifold is a locally product Riemannian manifold and investigate fundamental results on such submersion. We also ensure an explicit example of Clairaut semi invariant Riemannian submersion.

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23

Alshehri, Norah, and Mohammed Guediri. "Projective Vector Fields on Semi-Riemannian Manifolds." Mathematics 12, no. 18 (2024): 2914. http://dx.doi.org/10.3390/math12182914.

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This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function ψ and the vector field ζ dual to dψ does not change its causal character, then P is homothetic, or ζ is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the character

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24

Gündüzalp, Yılmaz, and Murat Polat. "Lagrangian and Clairaut anti-invariant semi-Riemannian submersions in para-Kaehler geometry." Boletim da Sociedade Paranaense de Matemática 42 (May 28, 2024): 1–12. http://dx.doi.org/10.5269/bspm.64600.

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Purpose of this article is to examine some geometric features of Clairaut anti-invariant semi-Riemannian submersions from para-Kaehler manifold to a Riemannian manifold. We give Lagrangian semi-Riemannian submersion in para-Kaehler space froms. Then, we investigate under what conditions Clairaut submersions can become anti-invariant semi-Riemannian submersions. After, we obtain conditions for totally geodesic on vertical and horizontal distributions. We also supply a non-trivial example of Clairaut submersion

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25

KUMAR, SACHIN, and AKHILESH YADAV. "Semi-Slant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds." Kragujevac Journal of Mathematics 49, no. 1 (2024): 141–58. http://dx.doi.org/10.46793/kgjmat2501.141k.

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The aim of our paper is to introduce the notion of semi-slant lightlike submanifolds of golden semi-Riemannian manifolds. We give non-trivial examples of semi-slant lightlike submanifolds and provide a characterization theorem of such submanifolds. Further, we obtain necessary and suﬃcient conditions for integrability of the distributions and investigate the geometry of the leaves of the foliation determined by the distributions. We also obtain a necessary and suﬃcient condition for the induced connection to be a metric connection. Finally, we obtain necessary and suﬃcient condition for mixed-

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26

Dogru, Yusuf. "$ \eta $-Ricci-Bourguignon solitons with a semi-symmetric metric and semi-symmetric non-metric connection." AIMS Mathematics 8, no. 5 (2023): 11943–52. http://dx.doi.org/10.3934/math.2023603.

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<abstract><p>We consider a generalization of a Ricci soliton as $ \eta $-Ricci-Bourguignon solitons on a Riemannian manifold endowed with a semi-symmetric metric and semi-symmetric non-metric connection. We find some properties of $ \eta $-Ricci-Bourguignon soliton on Riemannian manifolds equipped with a semi-symmetric metric and semi-symmetric non-metric connection when the potential vector field is torse-forming with respect to a semi-symmetric metric and semi-symmetric non-metric connection.</p></abstract>

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27

TAYEBI, A., E. PEYGHAN та B. NAJAFI. "ON SEMI-C-REDUCIBILITY OF (α, β)-METRICS". International Journal of Geometric Methods in Modern Physics 09, № 04 (2012): 1250038. http://dx.doi.org/10.1142/s0219887812500387.

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Every non-Riemannian (α, β)-metric on a manifold with dimension n ≥ 3 is semi-C-reducible. Thus the study on semi-C-reducible metrics will enhance our understanding on the physical meaning of (α, β)-metrics. In this paper, we study weakly Landsberg semi-C-reducible metrics with some non-Riemannian curvature properties. Then we find some conditions on semi-C-reducible manifolds under which the notions of isotropic Landsberg curvature and of isotropic mean Landsberg curvature are equivalent.

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28

Zangiabadi, Elham, and Zohreh Nazari. "Semi-Riemannian manifold with semi-symmetric connections." Journal of Geometry and Physics 169 (November 2021): 104341. http://dx.doi.org/10.1016/j.geomphys.2021.104341.

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29

Han, Yanling, Fengyun Fu, and Peibiao Zhao. "On semi-symmetric metric connection in sub-Riemannian manifold." Tamkang Journal of Mathematics 47, no. 4 (2016): 373–84. http://dx.doi.org/10.5556/j.tkjm.47.2016.1908.

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The authors firstly in this paper define a semi-symmetric metric non-holonomic connection (in briefly, SS-connection) on sub-Riemannian manifolds. An invariant under a SS-connection transformation is obtained. The authors then further give a result that a sub-Riemannian manifold $(M,V_{0},g,\bar{\nabla})$ is locally horizontally flat if and only if $M$ is horizontally conformally flat and horizontally Ricci flat.

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30

Kılıç, Erol, and Oğuzhan Bahadır. "Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/178390.

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We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical anti-invariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quarter-symmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

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31

Han, Yanling, Fengyun Fu, and Peibiao Zhao. "A class of non-holonomic projective connections on sub-Riemannian manifolds." Filomat 31, no. 5 (2017): 1295–303. http://dx.doi.org/10.2298/fil1705295h.

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The authors define a semi-symmetric non-holonomic (SSNH)-projective connection on sub-Riemannian manifolds and find an invariant of the SSNH-projective transformation. The authors further derive that a sub-Riemannian manifold is of projective flat if and only if the Schouten curvature tensor of a special SSNH-connection is zero.

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32

Stoica, O. C. "On singular semi-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 11, no. 05 (2014): 1450041. http://dx.doi.org/10.1142/s0219887814500418.

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On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no longer work, because they are based on the inverse of the metric, and on related operations like the contraction between covariant indices. In this paper, we develop the geometry of singular semi-Riemannian manifolds. First, we introduce an invariant and canonical contraction between covariant indices, applicable even for degenerate metrics. This contraction a

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33

Velimirović, Ljubica, Pradip Majhi, and Uday Chand De. "Almost pseudo-Q-symmetric semi-Riemannian manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 07 (2018): 1850117. http://dx.doi.org/10.1142/s0219887818501177.

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The object of the present paper is to study almost pseudo-[Formula: see text]-symmetric manifolds [Formula: see text]. Some geometric properties have been studied which recover some known results of pseudo [Formula: see text]-symmetric manifolds. We obtain a necessary and sufficient condition for the [Formula: see text]-curvature tensor to be recurrent in [Formula: see text]. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric [Formula: see text] is an Einstein manifold under certain condition. Moreover we deal with [Formula: see text]-flat perfect fluid

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34

Karatas, Esra, Semra Zeren, and Mustafa Altin. "Riemannian submersions endowed with a new type of semi-symmetric non-metric connection." Thermal Science 27, no. 4 Part B (2023): 3393–403. http://dx.doi.org/10.2298/tsci2304393k.

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In this paper we study relations for the covariant derivative of O?Neill?s tensor fields, Riemannian curvature, Ricci curvature and scalar curvature of the Riemannian submersion from a Riemannian manifold with respect to a new type of semi-symmetric non-metric connection to a Riemannian manifold, respectively, and demonstrate the relationship between them.

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35

Singh, Shalini. "A semi-symmetric metric connection on an integrated contact metric structure manifold." International Journal of Advances in Scientific Research 2, no. 12 (2016): 194. http://dx.doi.org/10.7439/ijasr.v2i12.3814.

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In 1924, A. Friedmann and J. A. Schoten [1] introduced the idea of a semi-symmetric linear connection in a differentiable manifold. Hayden [2] has introduced the idea of metric connection with torsion in a Riemannian manifold. The properties of semi-symmetric metric connection in a Riemannian manifold have been studied by Yano [3] and others [4], [5]. The purpose of the present paper is to study some properties of semi-symmetric metric connection on an integrated contact metric structure manifold [6], several useful algebraic and geometrical properties have been studied.

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36

Gupta, Punam. "On compact Einstein doubly warped product manifolds." Tamkang Journal of Mathematics 49, no. 4 (2018): 267–75. http://dx.doi.org/10.5556/j.tkjm.49.2018.2605.

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In this paper, the non-existence of connected, compact Einstein doubly warped product semi-Riemannian manifold with non-positive scalar curvature is proved. It is also shown that there does not exist non-trivial connected Einstein doubly warped product semi-Riemannian manifold with compact base $B$ or fibre $F$.

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37

Barletta, Elisabetta, Sorin Dragomir, and Francesco Esposito. "On the Canonical Foliation of an Indefinite Locally Conformal Kähler Manifold with a Parallel Lee Form." Mathematics 9, no. 4 (2021): 333. http://dx.doi.org/10.3390/math9040333.

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We study the semi-Riemannian geometry of the foliation F of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is the Lee form of M). If M is conformally flat then every leaf of F is shown to be a totally geodesic semi-Riemannian hypersurface in M, and a semi-Riemannian space form of sectional curvature c/4, carrying an indefinite c-Sasakian structure. As a corollary of the result together with a semi-Riemannian version of the de Rham decomposition theorem any geodesically complete, conformally flat, indefinite Vais

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38

Atkins, Richard. "Parallel metrics and reducibility of the holonomy group." Bulletin of the Australian Mathematical Society 74, no. 1 (2006): 45–68. http://dx.doi.org/10.1017/s0004972700035565.

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In this paper we investigate the relationship between the existence of parallel semi-Riemannian metrics of a connection and the reducibility of the associated holonomy group. The question as to whether the holonomy group necessarily reduces in the presence of a specified number of independent parallel semi-Riemannian metrics is completely determined by the the signature of the metrics and the dimension d of the manifold, when d ≠ 4. In particular, the existence of two independent, parallel semi-Riemannian metrics, one of which having signature (p,q) with p ≠ q, implies the holonomy group is re

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39

Lashin, El-Said R., and Tarek F. Mersal. "On hypersurfaces in a locally affine Riemannian Banach manifold II." International Journal of Mathematics and Mathematical Sciences 2004, no. 2 (2004): 99–104. http://dx.doi.org/10.1155/s0161171204203325.

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In our previous work (2002), we proved that an essential second-order hypersurface in an infinite-dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature. In this note, we prove the converse, in other words, we prove that a hypersurface of constant nonzero Riemannian curvature in a locally affine (flat) semi-Riemannian Banach space is an essential hypersurface of second order.

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40

Haji-Badali, Ali, and Amirhesam Zaeim. "Commutative curvature operators over four-dimensional homogeneous manifolds." International Journal of Geometric Methods in Modern Physics 12, no. 10 (2015): 1550123. http://dx.doi.org/10.1142/s0219887815501236.

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Four-dimensional pseudo-Riemannian homogeneous spaces whose isotropy is non-trivial with commuting curvature operators have been studied. The only example of homogeneous Einstein four-manifold which is curvature-Ricci commuting but not semi-symmetric has been presented. Non-trivial examples of semi-symmetric homogeneous four-manifolds which are not locally symmetric, also Jacobi–Jacobi commuting manifolds which are not flat have been presented.

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41

Tripathi, Mukut Mani, Erol Kılıç, Selcen Yüksel Perktaş, and Sadık Keleş. "Indefinite Almost Paracontact Metric Manifolds." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–19. http://dx.doi.org/10.1155/2010/846195.

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We introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para-Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an (ε)-para Sasakian structure. We show that, for an (ε)-para Sasakian manifold, the conditions of being symmetric, semi-symmetric, or of constant sectional curvature are all identical. It is shown that a symmetric spacelik

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42

Wu, Tong, and Yong Wang. "Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions." Symmetry 13, no. 1 (2021): 79. http://dx.doi.org/10.3390/sym13010079.

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In this work, the cases of non-integrable distributions in a Riemannian manifold with the first generalized semi-symmetric non-metric connection and the second generalized semi-symmetric non-metric connection are discussed. We obtain the Gauss, Codazzi, and Ricci equations in both cases. Moreover, Chen’s inequalities are also obtained in both cases. Some new examples based on non-integrable distributions in a Riemannian manifold with generalized semi-symmetric non-metric connections are proposed.

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43

Ida, Cristian, Alexandru Ionescu, and Adelina Manea. "A note on para-holomorphic Riemannian–Einstein manifolds." International Journal of Geometric Methods in Modern Physics 13, no. 09 (2016): 1650107. http://dx.doi.org/10.1142/s0219887816501073.

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The aim of this note is the study of Einstein condition for para-holomorphic Riemannian metrics in the para-complex geometry framework. First, we make some general considerations about para-complex Riemannian manifolds (not necessarily para-holomorphic). Next, using a one-to-one correspondence between para-holomorphic Riemannian metrics and para-Kähler–Norden metrics, we study the Einstein condition for a para-holomorphic Riemannian metric and the associated real para-Kähler–Norden metric on a para-complex manifold. Finally, it is shown that every semi-simple para-complex Lie group inherits a

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44

Iscan, Murat, and Gulnur Caglar. "Para-Kähler–Einstein structures on Walker 4-manifolds." International Journal of Geometric Methods in Modern Physics 13, no. 02 (2016): 1650006. http://dx.doi.org/10.1142/s0219887816500067.

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A 4-dimensional Walker manifold [Formula: see text] is a semi-Riemannian manifold [Formula: see text] of signature (++––) (or neutral), which admits a field of null 2-plane. The goal of this paper is to study certain almost paracomplex structures [Formula: see text] on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the para-Kähler forms are symplectic. We show that such a Walker 4-manifold can carry a class of indefinite para-Kähler–Einstein 4-manifolds, examples of indefinite para-Kähler 4-manifolds, and also almost indefinite para-Hermitian–Einstein

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45

DE, KRISHNENDU, UDAY CHAND DE, and AYDIN GEZER. "Investigations on a Riemannian Manifold with a Semi- Symmetric Non-Metric Connection and Gradient Solitons." Kragujevac Journal of Mathematics 49, no. 3 (2024): 387–400. http://dx.doi.org/10.46793/kgjmat2503.387d.

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This article carries out the investigation of a three-dimensional Riemannian manifold N3 endowed with a semi-symmetric type non-metric connection. Firstly, we construct a non-trivial example to prove the existence of a semi-symmetric type non-metric connection on N3. It is established that a N3 with the semi-symmetric type non-metric connection, whose metric is a gradient Ricci soliton, is a manifold of constant sectional curvature with respect to the semi-symmetric type non-metric connection. Moreover, we prove that if the Riemannian metric of N3 with the semi-symmetric type non-metric connec

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46

Srivastava, S. K., and Ajai Kumar Srivastava. "Generlized Quasi-Sasakian Manifold admitting Semi-Symmetric Non Metric Connection." Journal of the Tensor Society 2, no. 00 (2008): 83–89. http://dx.doi.org/10.56424/jts.v2i00.9962.

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Agashe and Chafle [4] defined a semi – symmetric non-etric connection in a Riemannian manifold. Further, the properties of semi- symmetric non-metric connection in almost contact metric manifold has been studied by Ojha and Prasad [5]. The purpose of this paper is to introduce a semi-symmetric non-metric connection in generalized quasi-sasakian manifold.

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47

Ahmad, Muqeem, and Mobin Ahmad. "A NOTE ON INTEGRABILITY CONDITIONS AND TOTALLY GEODESIC FOLIATIONS OF DISTRIBUTIONS ON A SEMI-SLANT LIGHTLIKE SUBMANIFOLD." South East Asian Journal of Mathematics and Mathematical Sciences 20, no. 02 (2024): 347–64. https://doi.org/10.56827/seajmms.2024.2002.25.

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In the present paper, we consider a golden semi-Riemannian manifold and find its semi-slant lightlike submanifolds. We examine the integrability of the distributions $D_{1},D_{2}$ and $Rad \texttt{TJ}$ defined on semi-slant lightlike submanifolds. Further, we investigate the conditions of the foliations of the distributions when they become totally geodesic. The goal of this study is to determine the semi-slant lightlike submanifolds of a golden semi-Riemannian manifold. The distributions $D_{1},D_{2}$, and $Rad \texttt{TJ}$ defined on semi-slant lightlike submanifolds are examined for integra

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48

Yucesan, Ahmet, and Erol Yasar. "SEMI-RIEMANNIAN SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION." Communications of the Korean Mathematical Society 27, no. 4 (2012): 781–93. http://dx.doi.org/10.4134/ckms.2012.27.4.781.

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49

Guan, Daniel. "A Classification of Compact Cohomogeneity One Locally Conformal Kähler Manifolds." Mathematics 12, no. 11 (2024): 1710. http://dx.doi.org/10.3390/math12111710.

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In this paper, we apply a result of the classification of a compact cohomogeneity one Riemannian manifold with a compact Lie group G to obtain a classification of compact cohomogeneity one locally conformal Kähler manifolds. In particular, we prove that the compact complex manifold is a complex one-dimensional torus bundle over a projective rational homogeneous, or cohomogeneity one manifold except of a class of manifolds with a generalized Hopf surface bundle over a projective rational homogeneous space. Additionally, it is a homogeneous compact complex manifold under the complexification GC

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50

Chaubey, S. K., and R. H. Ojha. "On a semi-symmetric non-metric connection." Filomat 25, no. 4 (2011): 19–27. http://dx.doi.org/10.2298/fil1104019c.

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Yano [1] defined and studied semi-symmetric metric connection in a Riemannian manifold and this was extended by De and Senguta [8] and many other geometers. Recently, the present authors [3], [5] defined semi-symmetric non-metric connections in an almost contact metric manifold. In this paper, we studied some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold.

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