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Relevant bibliographies by topics / Holomorphic curvature

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Journal articles

Academic literature on the topic 'Holomorphic curvature'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "Holomorphic curvature"

1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

Vanithalakshmi, S. M., S. K. Narasimhamurthy та M. K. Roopa. "On Holomorphic Curvature of Complex Finsler with special (α, β)−Metric". Journal of the Tensor Society 12, № 01 (2007): 33–48. http://dx.doi.org/10.56424/jts.v12i01.10593.

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The notion of the holomorphic curvature for a Complex Finsler space (M, F) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. This paper is about the fundamental metric tensor, inverse tensor and as a special approach of the pull-back bundle is devoted to obtain the Riemannian curvature and holomorphic curvature of Complex Finsler with special (α, β)-metric

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9

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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10

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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