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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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A sectional curvature for statistical structures [PDF]
Linear Algebra and its Applications, 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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Four-manifolds of Pinched Sectional Curvature [PDF]
Pacific Journal of Mathematics, 2019 In this paper, we study closed four-dimensional manifolds. In particular, we show that under various new pinching curvature conditions (for example, the sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue) then the manifold is ...
Cao, Xiaodong, Tran, Hung
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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.
Fulya Şahin +2 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
Sectional curvature and Weitzenbock formulae [PDF]
Indiana University Mathematics Journal, 2022 We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenböck formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the Kulkarni-Nomizu product, we provide a simple formula for such curvature terms.
Bettiol, R., Mendes, R.
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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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Remarks on symplectic sectional curvature [PDF]
Differential Geometry and its Applications, 2017 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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Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces [PDF]
, 2015 The main result of this note is that, for each $n\in \{1,2,3,\ldots\}$, there exists a Hodge metric on the $n$-th Hirzebruch surface whose positive holomorphic sectional curvature is $\frac{1}{(1+2n)^2}$-pinched.
Alvarez, Angelynn +2 more
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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.
Francis Owen +2 more
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