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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Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature. [PDF]
Entropy (Basel), 2018 In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties.
Decu S +3 more
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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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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 ...
B. Opozda
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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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Norden Golden Manifolds with Constant Sectional Curvature and Their Submanifolds
Mathematics, 2023 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.
F. Şahin, B. Şahin, F. Erdoğan
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Highly connected 7-manifolds and non-negative sectional curvature
Annals of Mathematics, 2020 Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that
S. Goette, M. Kerin, K. Shankar
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Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics [PDF]
Science China Mathematics, 2019 We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal Kähler manifold with constant nonpositive holomorphic sectional curvature is Kähler. We also give
Haojie Chen, Lin Chen, Xiaolan Nie
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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 ...
Shin-ichi Matsumura
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On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature [PDF]
Pure and Applied Mathematics Quarterly, 2018 In this paper, we pose several conjectures on structures and images of maximal rationally connected fibrations of smooth projective varieties admitting semi-positive holomorphic sectional curvature.
Shin-ichi Matsumura
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