Results 131 to 140 of about 14,803 (150)

A note on holomorphic sectional curvature of a hermitian manifold

Glasgow Mathematical Journal, 2022
As is well known, the holomorphic sectional curvature is just half of the sectional curvature in a holomorphic plane section on a Kähler manifold (Zheng, Complex differential geometry (2000)).
Hongjun Li, Chunhui Qiu
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Holomorphic sectional curvature, nefness and Miyaoka–Yau type inequality [PDF]

Mathematische Zeitschrift, 2018
On a compact K hler manifold, we introduce a notion of almost nonpositivity for the holomorphic sectional curvature, which by definition is weaker than the existence of a K hler metric with semi-negative holomorphic sectional curvature. We prove that a compact K hler manifold of almost nonpositive holomorphic sectional curvature has a nef canonical ...
Yashan Zhang
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The Holomorphic Statistical Structures of Constant Holomorphic Sectional Curvature on Complex Space Forms

Bulletin of the Iranian Mathematical Society
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mingming Yan, Xin Wu, Liang Zhang
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A note on almost abelian groups with constant holomorphic sectional curvature

Proceedings of the American Mathematical Society
A long-standing conjecture in non-Kähler geometry states that if the Chern (or Levi-Civita) holomorphic sectional curvature of a compact Hermitian manifold is a constant c c , then the metric must be Kähler when c ≠
Yulu Li, Fangyang Zheng
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Constant holomorphic sectional curvature conjecture and Fino-Vezzoni conjecture

Surveys in Differential Geometry
In this short essay, we will survey on two conjectures in non-K\"ahler geometry: the constant holomorphic sectional curvature conjecture and the Fino-Vezzoni conjecture. We aim at the broad audience and assume no expertise in non-K\"ahler geometry.
Fangyang Zheng
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Doubly warped product Hermitian manifold with constant holomorphic sectional curvature

Analysis
Let ( M 1 , g ) (M_{1},g) and ( M 2 , h ) (M_{2},h) be two Hermitian manifolds. Then the doubly warped product (abbreviated as DWP) Hermitian manifold of ( M 1 , g ) (M_{1},g) and ( M 2 , h ) (M_{2},h) is the product manifold M 1 × M 2 M_{1}\times M_{2 ...
Hui Zhang, Yong He, Weina Lu, Xiaohui Xu
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On holomorphic immersions into kähler manifolds of constant holomorphic sectional curvature

Science in China Series A: Mathematics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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HOLOMORPHIC SECTIONAL AND BISECTIONAL CURVATURES OF ALMOST HERMITIAN MANIFOLDS

SUT Journal of Mathematics, 1995
The study of the holomorphic sectional curvature of Kähler manifolds has been developed intensively and it provides many interesting results on the structure of these manifolds. Although many efforts have been devoted to the extension of those results to broader classes of manifolds, there are still two basic open questions: when does the pointwise ...
Hsiung, Chuan-Chih, Yang, Wenmao, Friedland, Lew   +2 more
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Holomorphic sectional curvatures of indefinite complex Grassmann manifolds

Mathematical Proceedings of the Cambridge Philosophical Society, 1983
In (2), indefinite Kählerian manifolds have been examined from the point of view of holomorphic sectional curvature. Examples in (2) show that the analogue of Kulkarni's theorem (see (4), p. 173) for the holomorphic sectional curvature is false and the best possible result in the direction is:Theorem 1 (known, (2)).
Montiel, Sebastian, Romero, Alfonso
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K-spaces of constant holomorphic sectional curvature

Mathematical Notes of the Academy of Sciences of the USSR, 1976
In this note we prove the equivalence of the pointwise constancy and the global constancy of the holomorphic sectional curvature of a K-space. A criterion for the constancy of the holomorphic sectional curvature of a K-space is found. It is proved that every proper K-space of constant holomorphic sectional curvature is a six-dimensional orientable ...
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