Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature [PDF]
Entropy, 2018 In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati
Simona Decu +3 more
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Complex nilmanifolds with constant holomorphic sectional curvature [PDF]
Proceedings of the American Mathematical Society, 2021 A well known conjecture in complex geometry states that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler if the constant is non-zero and must be Chern flat if the constant is zero.
Yulu Li, Fangyang Zheng
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Holomorphic Sectional Curvature of Complex Finsler Manifolds. [PDF]
J Geom Anal, 2019 In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold.
Wan X.
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Quasi-projective manifolds with negative holomorphic sectional curvature [PDF]
Duke mathematical journal, 2018 Let $(M,\omega)$ be a compact K\"ahler manifold with negative holomorphic sectional curvature. It was proved by Wu-Yau and Tosatti-Yang that $M$ is necessarily projective and has ample canonical bundle.
Henri Guenancia
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A sectional curvature for statistical structures [PDF]
, 2015 A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.Comment: 19 ...
Opozda, Barbara
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On the Tachibana numbers of closed manifolds with pinched negative sectional curvature
Дифференциальная геометрия многообразий фигур, 2020 Conformal Killing form is a natural generalization of conformal Killing vector field. These forms were extensively studied by many geometricians. These considerations were motivated by existence of various applications for these forms.
S.E. Stepanov, I. I. Tsyganok
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On projective manifolds with semi-positive holomorphic sectional curvature [PDF]
American Journal of Mathematics, 2018 :We establish structure theorems for a smooth projective variety $X$ with semi-positive holomorphic sectional curvature. We first prove that $X$ is rationally connected if $X$ has no truly flat tangent vectors at some point (which is satisfied when the ...
Shinichi Matsumura
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Hirzebruch manifolds and positive holomorphic sectional curvature [PDF]
Annales de l'Institut Fourier, 2019 This paper is the first step in a systematic project to study examples of Kahler manifolds with positive holomorphic sectional curvature ($H > 0$). Previously Hitchin proved that any compact Kahler surface with $H>0$ must be rational and he constructed ...
Bo Yang, Fangyang Zheng
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On the Topological Classification of Four-Dimensional Steady Gradient Ricci Solitons with Nonnegative Sectional Curvature [PDF]
MathematicsIn this paper, we study the topology of steady gradient Ricci solitons with nonnegative sectional curvature. We apply a characterization theorem for the fundamental group of a positively curved steady gradient Ricci soliton that admits a critical point ...
Yuehan Hao
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Curvature Pinching Problems for Compact Pseudo-Umbilical PMC Submanifolds in
Mathematics, 2023 Let Sm(c) denote a sphere with a positive constant curvature c and Mn(n≥3) be an n-dimensional compact pseudo-umbilical submanifold in a Riemannian product space Sm(c)×R with a nonzero parallel mean curvature vector (PMC), where R is a Euclidean line. In
Wang-Hua Qiu, Xin Zhan
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