Results 1 to 10 of about 47,483 (226)
An Algebraic Inequality with Applications to Certain Chen Inequalities
Axioms, 2021 We give a simple proof of the Chen inequality for the Chen invariant δ(2,…,2)︸k terms of submanifolds in Riemannian space forms.
Ion Mihai, Radu-Ioan Mihai
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Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms
Axioms, 2022 In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized ...
Yanlin Li +3 more
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On Chen invariants and inequalities in quaternionic geometry [PDF]
Journal of Inequalities and Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gabriel-Eduard Vilcu
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Recent Developments on the First Chen Inequality in Differential Geometry
Mathematics, 2023 One of the most fundamental interests in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of submanifolds and find their applications.
Bang-Yen Chen, Gabriel-Eduard Vîlcu
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Tsukuba Journal of Mathematics, 2001 If a Riemannian manifold \(M\) can be minimally and isometrically immersed into a Euclidean space then, by the Gauss equation, the Ricci curvature of \(M\) is nonpositive. The author shows by an example that the curvature condition is not sufficient, i.e.
Bogdan D Suceava
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A Generalization of K. T. Chen's Invariants for Paths Under Transformation Groups [PDF]
Transactions of the American Mathematical Society, 1962 In a series of papers [1; 2; 3; 4], K. T. Chen introduced and studied certain infinite series of numbers associated with paths in Euclidean n-space. These numbers were invariants under translations, and in [4] he proved that they uniquely characterize paths under translations.
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Geometric Inequalities for a Submanifold Equipped with Distributions
Mathematics, 2022 The article introduces invariants of a Riemannian manifold related to the mutual curvature of several pairwise orthogonal subspaces of a tangent bundle. In the case of one-dimensional subspaces, this curvature is equal to half the scalar curvature of the
Vladimir Rovenski
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A New Algebraic Inequality and Some Applications in Submanifold Theory
Mathematics, 2021 We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality.
Ion Mihai, Radu-Ioan Mihai
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Chen invariants for Riemannian submersions and their applications
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2022 In this paper, an optimal inequality involving the delta curvature is exposed. With the help of this inequality some characterizations about the vertical motion and the horizontal divergence are obtained.
GÜLBAHAR, Mehmet +2 more
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