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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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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.
europepmc +3 more sources
On the sectional curvature of lightlike submanifolds [PDF]
Journal of Inequalities and Applications, 2016 The main purpose of this paper is to show how to obtain rigidity theorems with the help of curvature invariants in submanifolds of a semi-Riemannian manifold.
Erol Kılıç, Mehmet Gülbahar
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Sectional curvature and Weitzenbock formulae [PDF]
Indiana University Mathematics Journal, 2017 We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenbock formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the Kulkarni-Nomizu product,
R. G. Bettiol, R. Mendes
semanticscholar +4 more sources
On the Sectional Curvature of Compact Hypersurfaces [PDF]
Proceedings of the American Mathematical Society, 1990 We establish a sufficient condition for compact hypersurfaces of a complete riemannian manifold to be spherical. It is well known, from the works of Jacobowitz, Jorge and Koutroufiotis, and others, that the maximum sectional curvature of such hypersurfaces can be estimated from the curvature of the ambient space and the outer radius.
Leslie Coghlan, Yoe Itokawa
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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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A sectional curvature for statistical structures [PDF]
Linear Algebra and its Applications, 2015 19 ...
B. Opozda
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Sectional Curvature in Riemannian Manifolds
The Mathematica Journal, 2020 The metric structure on a Riemannian or pseudo-Riemannian manifold is entirely determined by its metric tensor, which has a matrix representation in any given chart.
B. Healy +2 more
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Remarks on symplectic sectional curvature [PDF]
Differential Geometry and its Applications, 2016 In [11], I. M. Gelfand, V. Retakh, and M. Shubin defined the symplectic sectional curvature of a torsion-free connection preserving a symplectic form. The present article defines the corresponding notion of constant symplectic sectional curvature and characterizes this notion in terms of the curvature tensor of the symplectic connection and its ...
Daniel J. F. Fox
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Positive weighted sectional curvature [PDF]
Indiana University Mathematics Journal, 2014 In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field.
Lee Kennard, W. Wylie
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