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Journal articles on the topic 'Lorentzian a-Sasakian manifold'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Singh, G. P., S. S. Mishra, and P. Sharma. "A study on W9-curvature tensor within the framework of Lorentzian para-Sasakian manifold." Extracta Mathematicae 40, no. 1 (2025): 43–56. https://doi.org/10.17398/2605-5686.40.1.43.

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This article focuses on the study of Lorentzian para-Sasakian manifolds Mn . It demonstrates that a W9-semisymmetric Lorentzian para-Sasakian manifold is a W9-flat manifold. Additionally, we explore Lorentzian para-Sasakian manifolds that satisfy the ζ-W9-flat condition, revealing that they represent a special type of η-Einstein manifold. Furthermore, it is shown that a W9-flat Lorentzian para-Sasakian manifold is a flat manifold. We also investigate Lorentzian para-Sasakian manifolds that meet W9-recurrent and ϕ-W9-semisymmetric conditions, presenting several significant results from this ana

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2

Perktas, Selcen Yüksel, Erol Kiliç, and Sadik Keles. "Hypersurfaces of Lorentzian para-Sasakian manifolds." MATHEMATICA SCANDINAVICA 109, no. 1 (2011): 5. http://dx.doi.org/10.7146/math.scand.a-15174.

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In this paper we study the invariant and noninvariant hypersurfaces of $(1,1,1)$ almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an $(1,1,1)$ almost contact manifold admits an almost product structure. We investigate hypersurfaces of affinely cosymplectic and normal $(1,1,1)$ almost contact manifolds. It is proved that a noninvariant hypersurface of a Lorentzian almost paracontact manifold is an almost product metric manifold. Some necessary and sufficient conditions have been gi

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3

Perktaş, Selcen, Erol Kiliç, and Sadik Keleş. "Biharmonic Hypersurfaces of LP-Sasakian Manifolds." Annals of the Alexandru Ioan Cuza University - Mathematics 57, no. 2 (2011): 387–408. http://dx.doi.org/10.2478/v10157-011-0034-z.

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Biharmonic Hypersurfaces of LP-Sasakian Manifolds In this paper the biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds are studied. We firstly find the biharmonic equation for a hypersurface which admits the characteristic vector field of the Lorentzian para-Sasakian as the normal vector field. We show that a biharmonic spacelike hypersurface of a Lorentzian para-Sasakian manifold with constant mean curvature is minimal. The biharmonicity condition for a hypersurface of a Lorentzian para-Sasakian manifold is investigated when the characteristic vector field belongs to the tangent h

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4

Laha, Barnali, Bandana Das, and Arindam Bhattacharyya. "Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold." Acta Universitatis Sapientiae, Mathematica 5, no. 2 (2013): 157–68. http://dx.doi.org/10.2478/ausm-2014-0011.

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Abstract In this paper we prove some properties of the indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define D-totally geodesic and D⊥-totally geodesic contact CRsubmanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefin

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5

Ahmad, Arjumand, and Shamsur Rahman. "A Note on Transversal hypersurfaces of Lorentzian para-Sasakian manifolds with a Semi-Symmetric Non-Metric Connection." Journal of the Tensor Society 8, no. 01 (2007): 53–63. http://dx.doi.org/10.56424/jts.v8i01.10558.

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Transversal hypersurfaces of Lorentzian para-Sasakian manifold are defined. It is proved that the fundamental 2-form on the transversal hypersurfaces of Lorentzian para-Sasakian manifold with (f, g, u, v, λ)-structure are closed. In this paper it is shown that transversal hypersurfaces of Lorentzian para-Sasakian manifold admits a product structure with a semi symmetric non metric connection. It is shown that transversal hypersurfaces of Lorentzian para-Sasakian manifold with a semi symmetric non metric connection are closed

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6

Khan, M. N. I., U. C. De та M. A. Choudhary. "Liftings from Lorentzian α-Sasakian manifolds to tangent bundles". BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 118, № 2 (2025): 137–46. https://doi.org/10.31489/2025m2/137-146.

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The goal of the current study is to investigate the complete lift of Lorentzian α-Sasakian manifolds to the tangent bundle TM. We also examine the complete lift of the different four types of Lorentzian αSasakian manifolds and find that (TM,gC) is an η-Einstein manifold in each instance. In order to show that a Lorentzian α-Sasakian manifold exists on TM, a non-trivial example by means of partial differential equations is built in the final section.

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7

HASEEB, ABDUL, and SUDHAKAR K. CHAUBEY. "Lorentzian Para-Sasakian Manifolds and *-Ricci Solitons." Kragujevac Journal of Mathematics 48, no. 2 (2024): 167–79. http://dx.doi.org/10.46793/kgjmat2402.167h.

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We study the properties of Lorentzian para-Sasakian manifolds endowed with ∗-Ricci solitons and gradient ∗-Ricci solitons. Finally, the existence of ∗-Ricci soliton on a 4-dimensional Lorentzian para-Sasakian manifold is proved by constructing a non-trivial example

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8

Siddiqi, Mohd Danish. "On δ- Lorentzian trans Sasakian manifold with semi-symmetric metric connection". Boletim da Sociedade Paranaense de Matemática 39, № 5 (2021): 113–35. http://dx.doi.org/10.5269/bspm.41108.

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The aim of the present research is to study the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric connection. We have found the expressions for curvature tensors, Ricci curvature tensors and scalar curvature of the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric and metric connection. Also, we have discussed some results on quasi-projectively flat and ϕ-projectively flat manifolds endowed with a semi-symmetric-metric connection. It shown that the manifold satisfying¯R. ¯ S = 0,¯P, ¯ S = 0.Lastly, we have obtained the conditions for the δ-Lorentzian Trans Sas

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9

Lee, Ji-Eun. "Slant Curves and Contact Magnetic Curves in Sasakian Lorentzian 3-Manifolds." Symmetry 11, no. 6 (2019): 784. http://dx.doi.org/10.3390/sym11060784.

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In this article, we define Lorentzian cross product in a three-dimensional almost contact Lorentzian manifold. Using a Lorentzian cross product, we prove that the ratio of κ and τ − 1 is constant along a Frenet slant curve in a Sasakian Lorentzian three-manifold. Moreover, we prove that γ is a slant curve if and only if M is Sasakian for a contact magnetic curve γ in contact Lorentzian three-manifold M. As an example, we find contact magnetic curves in Lorentzian Heisenberg three-space.

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10

Rahman, Shamsur. "Characterization of Quarter Symmetric Non-Metric Connection on Transversal Hypersurfaces of Lorentzian para-Sasakian Manifolds." Journal of the Tensor Society 8, no. 01 (2007): 65–75. http://dx.doi.org/10.56424/jts.v8i01.10557.

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In the present paper, quarter symmetric non metric connection on transversal hypersurfaces of Lorentzian para-Sasakian manifold is defined. It is studied the characterization of connections for product structure and it is shown that each transversal hypersurfaces of Lorentzian para-Sasakian manifold admits an almost product Lorentzian structure on a quarter symmetric non metric connection. Some characterization of transversal hypersurfaces of Lorentzian paraSasakian manifold with a quarter symmetric non metric connection are studied which are closed.

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11

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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12

Liu, Haiming, Xiawei Chen, Jianyun Guan, and Peifu Zu. "Lorentzian approximations for a Lorentzian $ \alpha $-Sasakian manifold and Gauss-Bonnet theorems." AIMS Mathematics 8, no. 1 (2022): 501–28. http://dx.doi.org/10.3934/math.2023024.

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<abstract><p>In this paper, we define the Lorentzian approximations of a $ 3 $-dimensional Lorentzian $ \alpha $-Sasakian manifold. Moreover, we define the notions of the intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on Lorentzian surfaces and spacelike surfaces and the intrinsic Gaussian curvature of Lorentzian surfaces and spacelike surfaces away from characteristic points. Furthermore, we derive the expressions of those curvatures and prove Gauss-Bonnet theorems for the Lorentzian surfaces and spacelike surfaces in the Lorentzian $ \a

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13

Prakash, Amit, and Anjana Singh. "Quasi Conformal Curvature Tensor on a Lorentzian Para-Sasakian Manifold." Journal of the Tensor Society 3, no. 00 (2009): 59–70. http://dx.doi.org/10.56424/jts.v3i01.9972.

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In This paper, we consider quasi-conformally flat, quasi-conformally conservative and -quasi conformally flat Lorentzian para-sasakian manifold. It has also been proved that an Einstein Lorentzian para-sasakian manifold satisfying the relation R(X, Y). = 0, where is a quasi-conformal curvature tensor is locally isometric with a unit sphere.

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14

Prakash, Amit, and Anjana Singh. "Quasi Conformal Curvature Tensor on a Lorentzian Para-Sasakian Manifold." Journal of the Tensor Society 3, no. 01 (2009): 59–70. http://dx.doi.org/10.56424/jts.v3i00.9972.

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In This paper, we consider quasi-conformally flat, quasi-conformally conservative and -quasi conformally flat Lorentzian para-sasakian manifold. It has also been proved that an Einstein Lorentzian para-sasakian manifold satisfying the relation R(X, Y). = 0, where is a quasi-conformal curvature tensor is locally isometric with a unit sphere.

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15

Shah, Riddhi Jung. "On Ricci solitons in LP-Sasakian manifolds." BIBECHANA 17 (January 1, 2020): 110–16. http://dx.doi.org/10.3126/bibechana.v17i0.24341.

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In this paper we study Ricci solitons in Lorentzian para-Sasakian manifolds. It is proved that the Ricci soliton in a (2n+1)-dimensinal LP-Sasakian manifold is shrinking. It is also shown that Ricci solitons in an LP-Sasakian manifold satisfying the derivation conditions R(ξ,X).W2 =0,W2 (ξ,X).W4 =0 and W4 (ξ,X).W2=0 are shrinking but are steady for the condition W2 (ξ,X).S=0. Finally, we give an example of 3-dimensional LP-Sasakian manifold and prove that the Ricci soliton is expanding and shrinking in this manifold. BIBECHANA 17 (2020) 110-116

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16

Li, Yanlin, Arup Kumar Mallick, Arindam Bhattacharyya та Mića S. Stanković. "A Conformal η-Ricci Soliton on a Four-Dimensional Lorentzian Para-Sasakian Manifold". Axioms 13, № 11 (2024): 753. http://dx.doi.org/10.3390/axioms13110753.

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This paper focuses on some geometrical and physical properties of a conformal η-Ricci soliton (Cη-RS) on a four-dimension Lorentzian Para-Sasakian (LP-S) manifold. The first section presents an introduction to Cη-RS on LP-S manifolds, followed by a discussion of preliminary ideas about the LP-Sasakian manifold. In the subsequent sections, we establish several results pertaining to four-dimension LP-S manifolds that exhibit Cη-RS. Additionally, we consider certain conditions associated with Cη-RS on four-dimension LP-S manifolds. Besides these geometrical points of view, we consider this solito

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17

Kumar, Rajesh, Lalnunenga Colney, Samesh Shenawy, and Nasser Bin Bin Turki. "Tangent Bundles Endowed with Quarter-Symmetric Non-Metric Connection (QSNMC) in a Lorentzian Para-Sasakian Manifold." Mathematics 11, no. 19 (2023): 4163. http://dx.doi.org/10.3390/math11194163.

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The purpose of the present paper is to study the complete lifts of a QSNMC from an LP-Sasakian manifold to its tangent bundle. The lifts of the curvature tensor, Ricci tensor, projective Ricci tensor, and lifts of Einstein manifold endowed with QSNMC in an LP-Sasakian manifold to its tangent bundle are investigated. Necessary and sufficient conditions for the lifts of the Ricci tensor to be symmetric and skew-symmetric and the lifts of the projective Ricci tensor to be skew-symmetric in the tangent bundle are given. An example of complete lifts of four-dimensional LP-Sasakian manifolds in the

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18

Prasad, Rajendra, Shashikant Pandey, and Abdul Haseeb. "On a Lorentzian Sasakian manifold endowed with a quarter-symmetric metric connection." Annals of West University of Timisoara - Mathematics and Computer Science 57, no. 2 (2019): 61–76. http://dx.doi.org/10.2478/awutm-2019-0015.

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19

Haseeb, Abdul, та Rajendra Prasad. "On concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection". Acta et Commentationes Universitatis Tartuensis de Mathematica 22, № 2 (2019): 279–92. http://dx.doi.org/10.12697/acutm.2018.22.23.

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20

Arslan, K., U. C. De, C. Murathan, and A. Yıldız. "On a class of Lorentzian para-Sasakian manifold." Proceedings of the Estonian Academy of Sciences. Physics. Mathematics 55, no. 4 (2006): 210. http://dx.doi.org/10.3176/phys.math.2006.4.02.

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21

Pokhariyal, G. P. "CURVATURE TENSORS IN A LORENTZIAN PARA SASAKIAN MANIFOLD." Quaestiones Mathematicae 19, no. 1-2 (1996): 129–36. http://dx.doi.org/10.1080/16073606.1996.9631829.

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22

Prasad, B., та Subhash Chandra Singh. "A Semi-Symmetric Metric ξ-Connection in an LP-Sasakian Manifold". Journal of the Tensor Society 6, № 01 (2007): 203–17. http://dx.doi.org/10.56424/jts.v6i01.10448.

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Yano (1970) investiated a semi-symmetric metric connections in a Riemannian manifold and since then many authors studied this connection. Further Mishra and Pandey (1978) defined a semi-symmetric metric ξ-connection in almost contact manifold and obtained various geometrical properties. Following Mishra and Pandey (1978) we define semi-symmetric metric ξ-connection in Lorentzian Para-Sasakian manifold and study some propeties of curvature tensors.

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23

Rahman, Shamsur, and Jae-Bok Jun. "CR-SUBMANIFOLDS OF A NEARLY LORENTZIAN PARA-SASAKIAN MANIFOLD." Far East Journal of Mathematical Sciences (FJMS) 103, no. 3 (2018): 587–602. http://dx.doi.org/10.17654/ms103030587.

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24

Venkatesha, Venkatesha. "Quarter-symmetric metric connection on a Lorentzian alpha-Sasakian manifold." New Trends in Mathematical Science 2, no. 5 (2017): 69–79. http://dx.doi.org/10.20852/ntmsci.2017.156.

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25

Singh, Gajendra. "On almost semi-invariant submanifold of a Lorentzian Sasakian manifold." International Journal of Mathematical Analysis 14, no. 7 (2020): 361–70. http://dx.doi.org/10.12988/ijma.2020.912121.

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26

Hakami, Ali H., and Mohd Danish Siddiqi. "Properties of Anti-Invariant Submersions and Some Applications to Number Theory." Mathematics 11, no. 15 (2023): 3368. http://dx.doi.org/10.3390/math11153368.

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In this article, we investigate anti-invariant Riemannian and Lagrangian submersions onto Riemannian manifolds from the Lorentzian para-Sasakian manifold. We demonstrate that, for these submersions, horizontal distributions are not integrable and their fibers are not totally geodesic. As a result, they are not totally geodesic maps. The harmonicity of such submersions is also examined. We specifically prove that they are not harmonic when the Reeb vector field is horizontal. Finally, we provide an illustration of our findings and mention some number-theoretic applications for the same submersi

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27

Khan, Mohammad Nazrul Islam, Fatemah Mofarreh, Abdul Haseeb, and Mohit Saxena. "Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection." Symmetry 15, no. 8 (2023): 1553. http://dx.doi.org/10.3390/sym15081553.

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The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly, (LPS)n) to its tangent bundle TM associated with a Riemannian connection DC and a quarter-symmetric metric connection (QSMC) D¯C.

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Rahman, Shamsur, Jae-Bok Jun, and Arjumand Ahmad. "ON SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY LORENTZIAN PARA-SASAKIAN MANIFOLD." Far East Journal of Mathematical Sciences (FJMS) 96, no. 6 (2015): 709–24. http://dx.doi.org/10.17654/fjmsmar2015_709_724.

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29

Haseeb, Abdul, and Rajendra Prasad. "On a Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection." Novi Sad Journal of Mathematics 46, no. 2 (2016): 103–16. http://dx.doi.org/10.30755/nsjom.04279.

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30

Ahmad, Mobin. "CR-SUBMANIFOLDS OF A LORENTZIAN PARA-SASAKIAN MANIFOLD ENDOWED WITH A QUARTER SYMMETRIC METRIC CONNECTION." Bulletin of the Korean Mathematical Society 49, no. 1 (2012): 25–32. http://dx.doi.org/10.4134/bkms.2012.49.1.025.

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31

Ahmad, Mobin, S. Ali, and Janardan Prasad Ojha. "CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric non-metric connection." International Journal of Mathematical Analysis 7 (2013): 2401–6. http://dx.doi.org/10.12988/ijma.2013.212352.

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32

Ahmad, Mobin, Abdul Haseeb, Jae-Bok Jun, and M. Hasan Shahid. "$$\textit{CR}$$ CR -submanifolds and $$\textit{CR}$$ CR -products of a Lorentzian para-Sasakian manifold endowed with a quarter symmetric semi-metric connection." Afrika Matematika 25, no. 4 (2013): 1113–24. http://dx.doi.org/10.1007/s13370-013-0180-4.

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33

Shadab Ahmad Khan. "A New Type of (ϵ)- Lorentzian Para-Sasakian Manifolds". Communications on Applied Nonlinear Analysis 32, № 1s (2024): 399–411. http://dx.doi.org/10.52783/cana.v32.2204.

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The current investigation commences by introducing a novel category termed (ϵ)-Lorentzian para-Sasakian manifolds, employing the generalized symmetric metric connection of a specific type(α,β). Several fundamental outcomes concerning with these manifolds are derived. Subsequently, we delve into the examination of conformally flat and Weyl-semi-symmetric (ϵ)-Lorentzian para-Sasakian manifolds, utilizing the generalized symmetric metric connection of the type(α,β).

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34

Faghfouri, Morteza, and Sahar Mashmouli. "On anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds." Filomat 32, no. 10 (2018): 3465–78. http://dx.doi.org/10.2298/fil1810465f.

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In this paper, we study a semi-Riemannian submersion from Lorentzian almost (para) contact manifolds and find necessary and sufficient conditions for the characteristic vector field to be vertical or horizontal. We also obtain decomposition theorems for anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds onto Lorentzian manifolds.

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35

Mohammed, Mohammed, Ion Mihai, and Andreea Olteanu. "Pinching Results for Submanifolds in Lorentzian–Sasakian Manifolds Endowed with a Semi-Symmetric Non-Metric Connection." Mathematics 12, no. 23 (2024): 3651. http://dx.doi.org/10.3390/math12233651.

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We establish an improved Chen inequality involving scalar curvature and mean curvature and geometric inequalities for Casorati curvatures, on slant submanifolds in a Lorentzian–Sasakian space form endowed with a semi-symmetric non-metric connection. Also, we present examples of slant submanifolds in a Lorentzian–Sasakian space form.

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36

Yildiz, Ahmet, Mine Turan та Cengizhan Murathan. "A Class of Lorentzian α-Sasakian Manifolds". Kyungpook mathematical journal 49, № 4 (2009): 789–99. http://dx.doi.org/10.5666/kmj.2009.49.4.789.

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37

SAVITA S SHINDE, VIJAY. M.P, and SHIVAKUMAR MD. "A Study on Curvature in Lorentzian Generalized Sasakian-Space-Forms and Its Applications." International Journal for Research Publication and Seminar 10, no. 1 (2019): 92–101. https://doi.org/10.36676/jrps.v10.i1.1630.

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In this paper, we investigate the curvature properties of Lorentzian generalized Sasakian-space-forms. We establish the necessary and sufficient conditions for these manifolds to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric, exploring their interrelationships. Additionally, as an application of these theorems, we study the behavior of Ricci almost solitons on conformally flat Lorentzian generalized Sasakian-space-forms.

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38

Amit Prakash, Amit Prakash. "m - projective curvature tensor on a Lorentzian para – Sasakian manifolds." IOSR Journal of Mathematics 6, no. 1 (2013): 19–23. http://dx.doi.org/10.9790/5728-0611923.

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39

CHAUBEY, S. K., та Uday Chand DE. "Lorentzian para-Sasakian Manifolds Admitting a New Type of Quarter-symmetric Non-metric ξ-connection". International Electronic Journal of Geometry 12, № 2 (2019): 250–59. http://dx.doi.org/10.36890/iejg.548364.

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40

Anitha, B. S. "Some results on lorentzian α-sasakian manifolds". Louis Savenien Dupuis Journal of Multidisciplinary Research, 31 грудня 2024, 281–191. https://doi.org/10.21839/lsdjmr.2024.v3.193.

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The purpose of this work is to introduce Lorentzian -Sasakian manifolds to the concept of an extended -curvature tensor. This study’s findings include the demonstration of an extended Lorentzian -Sasakian manifold that satisfies certain requirements for the -curvature tensor. First we demonstrated that, it is local isometric to the hyperbolic space because a Lorentzian -Sasakian manifold satisfying is a space with constant curvature . Further, we proved that, Einstein manifolds are -semisymmetric Lorentzian -Sasakian manifolds. Additionally we validated that, the hyperbolic space is locally is

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41

Siddiqi, Mohd Danish, and Mehmet Akif Akyol. "$\eta$-RICCI SOLITONS AND GRADIENT RICCI SOLITONS ON $\delta$- LORENTZIAN TRANS-SASAKIAN MANIFOLDS." Facta Universitatis, Series: Mathematics and Informatics, October 9, 2021, 529. http://dx.doi.org/10.22190/fumi201010039s.

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The objective of the present research article is to study the $\delta$-Lorentzian trans-Sasakian manifolds conceding the $\eta$-Ricci solitons and gradient Ricci soliton. We shown that a symmetric second order covariant tensor in a $\delta$-Lorentzian trans-Sasakian manifold is a constant multiple of metric tensor. Also, we furnish an example of $\eta$-Ricci soliton on 3-diemsional $\delta$-Lorentzian trans-Sasakian manifold is provide in the region where $\delta$-Lorentzian trans-Sasakian manifold is expanding. Furthermore, we discuss some results based on gradient Ricci solitons on $3$-dimen

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Siddiqi, Mohd Danish, Sudhakar Kumar Chaubey, and Aliya Naaz Siddiqui. "Clairaut anti-invariant submersions from Lorentzian trans-Sasakian manifolds." Arab Journal of Mathematical Sciences, October 7, 2021. http://dx.doi.org/10.1108/ajms-05-2021-0106.

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Purpose The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study. Desig

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43

C.Patra and A.Bhattacharyya. "Quarter-Symmetric Metric Connection On Pseudosymmetric Lorentzian a−Sasakian Manifolds." April 20, 2013. https://doi.org/10.5281/zenodo.814575.

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The object of this paper is to introduce a quarter-symmetric metric connec- tion in a pseudosymmetric Lorentzian a-Sasakian manifold and to study of some properties of it. Also we shall discuss some properties of the Weyl-pseudosymmetric Lorentzian a−Sasakian manifold and Ricci-pseudosymmetric Lorentzian a−Sasakian manifold with respet to quarter-symmetric metric connection. We have given an example of pseudosymmetric Lorentzian a-Sasakian manifold with respect to quarter-symmetric metric connection.

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44

Haseeb, Abdul, and Rajendra Prasad. "\eta-RICCI SOLITONS IN LORENTZIAN \alpha-SASAKIAN MANIFOLDS." Facta Universitatis, Series: Mathematics and Informatics, November 1, 2020, 713. http://dx.doi.org/10.22190/fumi2003713h.

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In the present paper, we have studied $\eta$-Ricci solitons in Lorentzian \\ $\alpha-$Sasakian manifolds satisfying certain curvature conditions. The existence of $\eta-$Ricci soliton in a Lorentzian $\alpha-$Sasakian manifold has been proved by a concrete example.

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45

Alegre, Pablo. "Semi-invariant submanifolds of Lorentzian Sasakian manifolds." Demonstratio Mathematica 44, no. 2 (2011). http://dx.doi.org/10.1515/dema-2013-0307.

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AbstractIn this paper we introduce the notion of semi-invariant submanifolds of a Lorentzian almost contact manifold. We study their principal characteristics and the particular cases in which the manifold is a Lorentzian Sasakian manifold or a Lorentzian Sasakian space form.

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46

Barnali, Laha, and Bhattacharyya Arindam. "Totally Umbilical Hemislant Submanifolds of Lorentzian (a)-Sasakian Manifold." April 21, 2015. https://doi.org/10.5281/zenodo.815122.

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This paper is summarized as follows. In the first section we have given a brief history about slant and hemi-slant submanifold of Lorentzian (a)-Sasakian manifold. This section is followed by some preliminaries about Lorentzian (a)-Sasakian manifold.

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Majhi, Pradip, and Debabrata Kar. "ALMOST CONFORMAL RICCI SOLITONS ON LP-SASAKIAN MANIFOLDS." Facta Universitatis, Series: Mathematics and Informatics, December 13, 2024, 761. https://doi.org/10.22190/fumi240220050m.

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The object of the present paper is to classify almost conformal Ricci solitons on Lorentzian para-Sasakian manifolds. In this paper, we prove that such manifolds with infinitesimal contact vector field V is η-Einstein and the scalar curvature of the manifold is constant, where V is potential vector field. Moreover, we show that an almost conformal Ricci soliton on Lorentzian para-Sasakian manifold becomes a conformal Ricci soliton and it is shrinking, steady or expanding according as the dimension of the manifold is greater than 3 or equal to 3 or less than 3. Also we prove that V is strictly

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48

Ahmad, Mobin, and Mahtab Alam. "LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE LORENTZIAN PARA-SASAKIAN STATISTICAL MANIFOLD." Facta Universitatis, Series: Mathematics and Informatics, December 20, 2023, 697. http://dx.doi.org/10.22190/fumi220908045a.

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In this paper, we introduce an indefinite LP-Sasakian statistical manifold and study lightlike submanifold of an indefinite LP-Sasakian statistical manifold. We also introduce some relations among induced geometrical objects with respect to dual connections in a lightlike submanifold of an indefinite LP-Sasakian statistical manifold. One example related to this concept is also presented. Finally, we show that an invariant lightlike submanifold of an indefinite LP-Sasakian statistical manifold is an indefinite LP-Sasakian statistical manifold.

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49

SARI, Ramazan, and İnan ÜNAL. "On Curvatures of Semi-invariant Submanifolds of Lorentzian Para-Sasakian Manifolds." Turkish Journal of Mathematics and Computer Science, December 13, 2023. http://dx.doi.org/10.47000/tjmcs.1322351.

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A Lorentzian para-Sasakian (LP-Sasakian) space form is a kind of para-Sasakian manifold with constant $ \varphi- $ holomorphic sectional curvature. The presented paper is on the curvatures of semi-invariant submanifolds of a LP-Sasakian space form. Firstly, the definition of a semi-invariant submanifold of LP-Sasakian space form is given and an example is presented. Then, using Gauss equation related to curvatures used for obtaining some important results on Ricci and scalar curvatures. Moreover, by suffering from these results conditions of distributions being Einstein have been examined. Fin

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Acet, Bilal Eftal. "f−BIHARMONIC CURVES WITH TIMELIKE NORMAL VECTOR ON LORENTZIAN SPHERE." Facta Universitatis, Series: Mathematics and Informatics, May 28, 2020, 311. http://dx.doi.org/10.22190/fumi2002311a.

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In this paper, we study $f-$biharmonic curves as the critical points of the $f-$bienergy functional $E_{2}(\psi )=\int_{M}f\mid \tau (\psi )^{2}\mid \vartheta _{g}$, on a Lorentzian para-Sasakian manifold $M$. We give necessary and sufficient conditions for a curve such that has a timelike principal normal vector on lying a $4$-dimensional conformally flat, quasi-conformally flat and conformally symmetric Lorentzian para-Sasakian manifold to be an $f-$biharmonic curve. Moreover, we introduce proper $f-$biharmonic curves on the Lorentzian sphere $S_{1}^{4}.$

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