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Journal articles on the topic 'Φ -holomorphic sectional curvature'

Author: Grafiati

Published: 7 June 2025

Last updated: 17 July 2025

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1

Abu-Saleem, Ahmad, A. R. Rustanov та S. V. Kharitonova. "AXIOM OF Φ-HOLOMORPHIC (2r+1)-PLANES FOR GENERALIZED KENMOTSU MANIFOLDS". Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, № 66 (2020): 5–23. http://dx.doi.org/10.17223/19988621/66/1.

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In this paper we study generalized Kenmotsu manifolds (shortly, a GK-manifold) that satisfy the axiom of Φ-holomorphic (2r+1)-planes. After the preliminaries we give the definition of generalized Kenmotsu manifolds and the full structural equation group. Next, we define Φ- holomorphic generalized Kenmotsu manifolds and Φ-paracontact generalized Kenmotsu manifold give a local characteristic of this subclasses. The Φ-holomorphic generalized Kenmotsu manifold coincides with the class of almost contact metric manifolds obtained from closely cosymplectic manifolds by a canonical concircular transfo

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2

Abood, Habeeb Mtashar, та Farah Al-Hussaini. "Locally Conformal Almost Cosymplectic Manifold of Φ-holomorphic Sectional Conharmonic Curvature Tensor". European Journal of Pure and Applied Mathematics 11, № 3 (2018): 671–81. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3261.

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The aim of the present paper is to study the geometry of locally conformal almost cosymplectic manifold of Φ-holomorphic sectional conharmonic curvature tensor. In particular, the necessaryand sucient conditions in which that locally conformal almost cosymplectic manifold is a manifold of point constant Φ-holomorphic sectional conharmonic curvature tensor have been found. The relation between the mentioned manifold and the Einstein manifold is determined.

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3

Kumar, S., and K. K. Dube. "Semi Invariant Submanifolds of a Para Kenmotsu Manifold with Constant \phi Holomorphic Sectional Curvature." Journal of the Tensor Society 2, no. 00 (2008): 7–16. http://dx.doi.org/10.56424/jts.v2i00.9955.

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In this Paper We have studied submanifolds para Kenmostu manifold to be semi-invarient submanifold. In particular case when it is a para Kenmostu space form of constant φ holomorphic sectional curvature

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4

Sharma, Gaurav, Sangeet Kumar, and Manoj Kumar. "On Lightlike Submersion of Radical Transversal Lightlike Submanifolds of a Kaehler Manifold." ECS Transactions 107, no. 1 (2022): 10069–84. http://dx.doi.org/10.1149/10701.10069ecst.

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The aim of present study is to introduce the idea of a lightlike submersion onto an indefinite almost Hermitian manifold from a radical transversal lightlike submanifold of an indefinite Kaehler manifold. We show that if an indefinite almost Hermitian manifold B admits a lightlike submersion φ : K → B of a radical transversal lightlike submanifold K of an indefinite Kaehler manifold then B must be an indefinite Kaehler manifold. We also establish the relation between the holomorphic sectional and holomorphic bisectional curvature of Κ and B.

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5

Rustanov, Aligadzhi Rabadanovich, Galina Vasilyevna Teplyakova та Svetlana Vladimirovna Kharitonova. "Nearly trans-Sasakian almost 𝐶(𝜆)-manifolds". Chebyshevskii Sbornik 24, № 5 (2024): 153–66. https://doi.org/10.22405/2226-8383-2023-24-5-153-166.

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The nearly trans-Sasakian manifolds, which are almost 𝐶(𝜆)-manifolds, are considered. On the space of the adjoint G-structure, the components of the Riemannian curvature tensor, the Ricci tensor of the nearly trans-Sasakian manifolds, and the almost 𝐶(𝜆)-manifolds are obtained.Identities are obtained that are satisfied by the Ricci tensor of nearly trans-Sasakian manifolds.It is proved that a Ricci-flat almost 𝐶(𝜆)-manifold is locally equivalent to the product of a Ricciflat K¨ahler manifold and a real line. Identities are obtained that are satisfied by the Ricci tensor of an almost 𝐶(𝜆)-manif

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6

Jain, Varun, Rachna Rani, Rakesh Kumar, and R. K. Nagaich. "Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds." International Journal of Geometric Methods in Modern Physics 14, no. 03 (2017): 1750034. http://dx.doi.org/10.1142/s0219887817500347.

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We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Sasakian manifold and obtain some characterization theorems on holomorphic sectional and holomorphic bisectional curvature.

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7

Kumar, Sangeet, Rakesh Kumar, and R. K. Nagaich. "Characterization of Holomorphic Bisectional Curvature ofGCR-Lightlike Submanifolds." Advances in Mathematical Physics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/356263.

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We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of aGCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature ofGCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for aGCR-lightlike submanifold of an indefinite complex space form to be null holomorphically flat. We also obtain some characterization theorems for holomorphic sectional and holomorphic bisectional curvature.

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8

Sekigawa, Kouei, and Takashi Koda. "Compact Hermitian surfaces of pointwise constant holomorphic sectional curvature." Glasgow Mathematical Journal 37, no. 3 (1995): 343–49. http://dx.doi.org/10.1017/s0017089500031621.

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Let M = (M, J, g) be an almost Hermitian manifold and U(M)the unit tangent bundle of M. Then the holomorphic sectional curvature H = H(x) can be regarded as a differentiable function on U(M). If the function H is constant along each fibre, then M is called a space of pointwise constant holomorphic sectional curvature. Especially, if H is constant on the whole U(M), then M is called a space of constant holomorphic sectional curvature. An almost Hermitian manifold with an integrable almost complex structure is called a Hermitian manifold. A real 4-dimensional Hermitian manifold is called a Hermi

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9

Ali A. Shihab and Rana H. jasim. "K- constant type Kahler and Nearly Kahler manifolds for conharmonic curvature tensor." Tikrit Journal of Pure Science 21, no. 1 (2023): 107–11. http://dx.doi.org/10.25130/tjps.v21i1.959.

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The constant of permanence conharmonic type kahler and nearly kahler manifold conditions are obtained when the Nearly Kahler manifold is a manifold conharmonic constant type (K). and also proved that M nearly kahler manifold of pointwise constant holomorphic sectional conharmonic (PHKm(X)) – curvature) curvature tensor if the components of holomorphic sectional (HS- curvature) curvature tensor in the adjoint G-structure space that satisfies condition .

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10

Şahin, Fulya, Bayram Şahin, and Feyza Esra Erdoğan. "Norden Golden Manifolds with Constant Sectional Curvature and Their Submanifolds." Mathematics 11, no. 15 (2023): 3301. http://dx.doi.org/10.3390/math11153301.

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This paper discusses the Norden golden manifold having a constant sectional curvature. First, it is shown that if a Norden golden manifold has a constant real sectional curvature, the manifold is flat. For this reason, the notions of holomorphic-like sectional curvature and holomorphic-like bisectional curvature on the Norden golden manifold are investigated, but it is seen that these notions do not work on the Norden golden manifold. This shows the need for a new concept of sectional curvature. In this direction, a new notion of sectional curvature (Norden golden sectional curvature) is propo

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11

Druţă-Romaniuc, S. L. "A Study on the Para-Holomorphic Sectional Curvature of Para-Kähler Cotangent Bundles." Annals of the Alexandru Ioan Cuza University - Mathematics 61, no. 1 (2015): 253–62. http://dx.doi.org/10.2478/aicu-2014-0033.

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Abstract We obtain the conditions under which the total space T *M of the cotangent bundle, endowed with a natural diagonal para-Kähler structure (G, P), has constant para-holomorphic sectional curvature. Moreover we prove that (T *M,G, P) cannot have nonzero constant para-holomorphic sectional curvature.

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12

Yu, Chengjie. "A Liouville Property of Holomorphic Maps." Scientific World Journal 2013 (2013): 1–3. http://dx.doi.org/10.1155/2013/265752.

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We prove a Liouville property of holomorphic maps from a complete Kähler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kähler manifold with a certain assumption on the sectional curvature.

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13

Rao, Pei Pei, and Fang Yang Zheng. "Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature." Acta Mathematica Sinica, English Series 38, no. 6 (2022): 1094–104. http://dx.doi.org/10.1007/s10114-022-1046-1.

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14

Gadea, Pedro, and Ángel Montesinos-Amilibia. "Spaces of constant para-holomorphic sectional curvature." Pacific Journal of Mathematics 136, no. 1 (1989): 85–101. http://dx.doi.org/10.2140/pjm.1989.136.85.

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15

Wong, Pit-Mann, Damin Wu, and Shing-Tung Yau. "Picard number, holomorphic sectional curvature, and ampleness." Proceedings of the American Mathematical Society 140, no. 2 (2012): 621–26. http://dx.doi.org/10.1090/s0002-9939-2011-10928-6.

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16

McNeal, Jeffery D. "Holomorphic sectional curvature of some pseudoconvex domains." Proceedings of the American Mathematical Society 107, no. 1 (1989): 113. http://dx.doi.org/10.1090/s0002-9939-1989-0979051-x.

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17

Wan, Xueyuan. "Holomorphic Sectional Curvature of Complex Finsler Manifolds." Journal of Geometric Analysis 29, no. 1 (2018): 194–216. http://dx.doi.org/10.1007/s12220-018-9985-6.

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18

Sato, Takuji, and Kouei Sekigawa. "Hermitian surfaces of constant holomorphic sectional curvature." Mathematische Zeitschrift 205, no. 1 (1990): 659–68. http://dx.doi.org/10.1007/bf02571270.

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19

Yang, Bo, and Fangyang Zheng. "Hirzebruch manifolds and positive holomorphic sectional curvature." Annales de l'Institut Fourier 69, no. 6 (2019): 2589–634. http://dx.doi.org/10.5802/aif.3303.

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20

Decu, Simona, Stefan Haesen, and Leopold Verstraelen. "Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature." Mathematics 8, no. 2 (2020): 251. http://dx.doi.org/10.3390/math8020251.

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In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant holomorphic sectional curvature. Moreover, we study the equality cases of such inequalities. An example on these submanifolds is presented.

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21

Bagewadi, C. S., та S. Venkatesha. "On Projective φ-Recurrent Kenmotsu Manifolds". Mapana - Journal of Sciences 4, № 2 (2005): 15–21. http://dx.doi.org/10.12723/mjs.7.3.

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In this paper we study a projective φ- recurrent Kenmotsu manifold and show that projective φ- recurrent Kenmotsu manifold having a non-zero constant sectional curvature is locally projective φ-symmetric.

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22

Mok, Ngaiming. "On holomorphic immersions into kähler manifolds of constant holomorphic sectional curvature." Science in China Series A: Mathematics 48, S1 (2005): 123–45. http://dx.doi.org/10.1007/bf02884700.

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23

Aydın, Muhittin Evren, Adela Mihai, and Cihan Özgür. "Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms." Axioms 11, no. 2 (2022): 59. http://dx.doi.org/10.3390/axioms11020059.

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We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1. By using this definition, we prove in Riemannian setting that if an isoparametric hypersurface is Pythagorean, then it is totally umbilical with sectional curvature φ+c, where φ is the Golden Ratio. We also extend this result to Lorentzian ambient space, observing the existence of a non totally umbilical model.

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24

SIDDIQUI, ALIYA NAAZ, and MOHAMMAD HASAN SHAHID. "Optimizations on Statistical Hypersurfaces with Casorati Curvatures." Kragujevac Journal of Mathematics 45, no. 03 (2021): 449–63. http://dx.doi.org/10.46793/kgjmat2103.449s.

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In the present paper, we study Casorati curvatures for statistical hypersurfaces. We show that the normalized scalar curvature for any real hypersurface (i.e., statistical hypersurface) of a holomorphic statistical manifold of constant holomorphic sectional curvature k is bounded above by the generalized normalized δ−Casorati curvatures and also consider the equality case of the inequality. Some immediate applications are discussed.

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25

Li, Shuwen, Yong He, Weina Lu, and Ruijia Yang. "Chern Flat and Chern Ricci-Flat Twisted Product Hermitian Manifolds." Mathematics 12, no. 3 (2024): 449. http://dx.doi.org/10.3390/math12030449.

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Let (M1,g) and (M2,h) be two Hermitian manifolds. The twisted product Hermitian manifold (M1×M2f,G) is the product manifold M1×M2 endowed with the Hermitian metric G=g+f2h, where f is a positive smooth function on M1×M2. In this paper, the Chern curvature, Chern Ricci curvature, Chern Ricci scalar curvature and holomorphic sectional curvature of the twisted product Hermitian manifold are derived. The necessary and sufficient conditions for the compact twisted product Hermitian manifold to have constant holomorphic sectional curvature are obtained. Under the condition that the logarithm of the

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26

Sato, Takuji. "Almost Kahler manifolds of constant holomorphic sectional curvature." Tsukuba Journal of Mathematics 20, no. 2 (1996): 517–24. http://dx.doi.org/10.21099/tkbjm/1496163099.

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27

SATO, TAKUJI, and KOUEI SEKIGAWA. "HERMITIAN SURFACES OF CONSTANT HOLOMORPHIC SECTIONAL CURVATURE II." Tamkang Journal of Mathematics 23, no. 2 (1992): 137–43. http://dx.doi.org/10.5556/j.tkjm.23.1992.4536.

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   The present paper ss a continuation of our previous work [7]. We shall prove that a compact Hernutian surface of pointwise positive constant holomorphic sectional curvature is biholomorphica.lly equivalent to a complex projective surface.   

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28

Sekigawa, Kouei, and Takuji Sato. "Nearly Kähler manifolds with positive holomorphic sectional curvature." Kodai Mathematical Journal 8, no. 2 (1985): 139–56. http://dx.doi.org/10.2996/kmj/1138037043.

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29

Lluch, Ana, and Vicente Miquel. "Kähler tubes of constant radial holomorphic sectional curvature." Manuscripta Mathematica 94, no. 1 (1997): 445–63. http://dx.doi.org/10.1007/bf02677866.

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30

Balas, Andrew. "Compact Hermitian manifolds of constant holomorphic sectional curvature." Mathematische Zeitschrift 189, no. 2 (1985): 193–210. http://dx.doi.org/10.1007/bf01175044.

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31

Heier, Gordon, Steven S. Y. Lu, and Bun Wong. "Kähler manifolds of semi-negative holomorphic sectional curvature." Journal of Differential Geometry 104, no. 3 (2016): 419–41. http://dx.doi.org/10.4310/jdg/1478138548.

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32

Fujimura, Shigeyoshi. "Indefinite Kähler metrics of constant holomorphic sectional curvature." Journal of Mathematics of Kyoto University 30, no. 3 (1990): 493–516. http://dx.doi.org/10.1215/kjm/1250520027.

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33

Abood, Habeeb M., and Nawaf J. Mohammed. "NEARLY COSYMPLECTIC MANIFOLD OF HOLOMORPHIC SECTIONAL CURVATURE TENSOR." Far East Journal of Mathematical Sciences (FJMS) 106, no. 1 (2018): 171–81. http://dx.doi.org/10.17654/ms106010171.

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34

Yang, Xiaokui. "Hermitian manifolds with semi-positive holomorphic sectional curvature." Mathematical Research Letters 23, no. 3 (2016): 939–52. http://dx.doi.org/10.4310/mrl.2016.v23.n3.a17.

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35

YAN, RONGMU. "COMPLEX BERWALD MANIFOLDS WITH VANISHING HOLOMORPHIC SECTIONAL CURVATURE." Glasgow Mathematical Journal 50, no. 2 (2008): 203–8. http://dx.doi.org/10.1017/s001708950800414x.

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AbstractIn this paper, we prove that a strongly convex and Kähler-Finsler metric is a complex Berwald metric with zero holomorphic sectional curvature if and only if it is a complex locally Minkowski metric.

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36

Bejan, Cornelia-Livia, and Michele Benyounes. "Kähler manifolds of quasi-constant holomorphic sectional curvature." Journal of Geometry 88, no. 1-2 (2008): 1–14. http://dx.doi.org/10.1007/s00022-007-1934-7.

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37

Chen, Shuwen, and Fangyang Zheng. "Canonical metric connections with constant holomorphic sectional curvature." Pacific Journal of Mathematics 334, no. 2 (2025): 329–48. https://doi.org/10.2140/pjm.2025.334.329.

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38

Siddiqui, Aliya, and Mohammad Shahid. "On totally real statistical submanifolds." Filomat 32, no. 13 (2018): 4473–83. http://dx.doi.org/10.2298/fil1813473s.

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In the present paper, first we prove some results by using fundamental properties of totally real statistical submanifolds immersed into holomorphic statistical manifolds. Further, we obtain the generalizedWintgen inequality for Lagrangian statistical submanifolds of holomorphic statistical manifolds with constant holomorphic sectional curvature c. The paper finishes with some geometric consequences of obtained results.

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39

Indiwar, Singh Chauhan, and S. Chauhan T. "D-homothetic deformation of an h-Einstein Para-Sasakian manifold." Indian Journal of Science and Technology 13, no. 13 (2020): 1435–39. https://doi.org/10.17485/IJST/v13i13.198.

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Abstract <strong>Objectives:</strong> The main purpose of this paper is to study the theory of Dhomothetic deformation of an h-Einstein Para-Sasakian manifold. <strong>Methods: </strong>A deformation technique is employed to solve the resulting problem. We provide its application in the general theory of relativity. Findings: Section 2 deals with recurrent and symmetric Para-Sasakian Manifolds. In section 3 we have defined and studied projectively symmetric Para-Sasakian manifold. The notion of ϕ -holomorphic sectional curvature in an h-Einstein Para-Sasakian manifold has been d

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40

Siddiqui, Aliya Naaz, Meraj Ali Khan, and Amira Ishan. "Contact CR $ \delta $-invariant: an optimal estimate for Sasakian statistical manifolds." AIMS Mathematics 9, no. 10 (2024): 29220–34. http://dx.doi.org/10.3934/math.20241416.

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<p>Chen (1993) developed the theory of $ \delta $-invariants to establish novel necessary conditions for a Riemannian manifold to allow a minimal isometric immersion into Euclidean space. Later, Siddiqui et al. (2024) derived optimal inequalities involving the CR $ \delta $-invariant for a generic statistical submanifold in a holomorphic statistical manifold of constant holomorphic sectional curvature. In this work, we extend the study of such optimal inequality to the contact CR $ \delta $-invariant on contact CR-submanifolds in Sasakian statistical manifolds of constant $ \phi $-sectio

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41

Bashir, M. A. "On totally umbilicalCR-submanifolds of a Kaehler manifold." International Journal of Mathematics and Mathematical Sciences 16, no. 2 (1993): 405–8. http://dx.doi.org/10.1155/s016117129300050x.

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LetMbe a compact3-dimensional totally umbilicalCR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector ofMdoes not vanish, thenMis either diffeomorphic toS3orRP3or a lens spaceLp,q3.

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42

Ali, Danish, Johann Davidov, and Oleg Mushkarov. "Holomorphic curvatures of twistor spaces." International Journal of Geometric Methods in Modern Physics 11, no. 03 (2014): 1450022. http://dx.doi.org/10.1142/s0219887814500224.

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We study the twistor spaces of oriented Riemannian 4-manifolds as a source of almost Hermitian 6-manifolds of constant or strictly positive holomorphic, Hermitian and orthogonal bisectional curvatures. In particular, we obtain explicit formulas for these curvatures in the case when the base manifold is Einstein and self-dual, and observe that the "squashed" metric on ℂℙ3 is a non-Kähler Hermitian–Einstein metric of positive holomorphic bisectional curvature. This shows that a recent result of Kalafat and Koca [M. Kalafat and C. Koca, Einstein–Hermitian 4-manifolds of positive bisectional curva

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43

Chen, Xiaoyang. "Stein manifolds of nonnegative curvature." Advances in Geometry 18, no. 3 (2018): 285–87. http://dx.doi.org/10.1515/advgeom-2016-0025.

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AbstractLet X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ*g = g.

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44

Sari, Ramazan. "Some Properties Curvture of Lorentzian Kenmotsu Manifolds." Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 283–92. http://dx.doi.org/10.2478/amns.2020.1.00026.

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AbstractIn this paper different curvature tensors on Lorentzian Kenmotsu manifod are studied. We investigate constant ϕ–holomorphic sectional curvature and ℒ-sectional curvature of Lorentzian Kenmotsu manifolds, obtaining conditions for them to be constant of Lorentzian Kenmotsu manifolds in such condition. We calculate the Ricci tensor and scalar curvature for all the cases. Moreover we investigate some properties of semi invariant submanifolds of a Lorentzian Kenmotsu space form. We show that if a semi-invariant submanifold of a Lorentzian Kenmotsu space form M is totally geodesic, then M is

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45

Oproiu, Vasile. "A Kähler Einstein structure on the tangent bundle of a space form." International Journal of Mathematics and Mathematical Sciences 25, no. 3 (2001): 183–95. http://dx.doi.org/10.1155/s0161171201002009.

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We obtain a Kähler Einstein structure on the tangent bundle of a Riemannian manifold of constant negative curvature. Moreover, the holomorphic sectional curvature of this Kähler Einstein structure is constant. Similar results are obtained for a tube around zero section in the tangent bundle, in the case of the Riemannian manifolds of constant positive curvature.

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46

Massamba, Fortuné, and Arthur Nzunogera. "A Note on Nearly Sasakian Manifolds." Mathematics 11, no. 12 (2023): 2634. http://dx.doi.org/10.3390/math11122634.

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A class of nearly Sasakian manifolds is considered in this paper. We discuss the geometric effects of some symmetries on such manifolds and show, under a certain condition, that the class of Ricci semi-symmetric nearly Sasakian manifolds is a subclass of Einstein manifolds. We prove that a Codazzi-type Ricci nearly Sasakian space form is either a Sasakian manifold with a constant ϕ-holomorphic sectional curvature H=1 or a 5-dimensional proper nearly Sasakian manifold with a constant ϕ-holomorphic sectional curvature H>1. We also prove that the spectrum of the operator H2 generated by the ne

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47

Galaev, S. V. "Almost contact Kähler manifolds of constant holomorphic sectional curvature." Russian Mathematics 58, no. 8 (2014): 35–42. http://dx.doi.org/10.3103/s1066369x14080040.

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48

Matsumura, Shin-ichi. "On projective manifolds with semi-positive holomorphic sectional curvature." American Journal of Mathematics 144, no. 3 (2022): 747–77. http://dx.doi.org/10.1353/ajm.2022.0015.

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49

Chen, Xinxiang, and Rongmu Yan. "CHARACTERIZING COMPLEX LOCALLY MINKOWSKI SPACES BY HOLOMORPHIC SECTIONAL CURVATURE." Bulletin of the Korean Mathematical Society 49, no. 1 (2012): 49–55. http://dx.doi.org/10.4134/bkms.2012.49.1.049.

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50

Lee, Jae. "Constancy of Holomorphic Sectional Curvature for Indefinite S- Manifolds." British Journal of Mathematics & Computer Science 1, no. 3 (2011): 121–28. http://dx.doi.org/10.9734/bjmcs/2011/270.

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