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Curvature tensors in riemannian manifold—II
Proceedings of the Indian Academy of Sciences - Section A, 1974In a recent paper author and Mishra [1] have studied the recurrent properties of conformal curvature tensor, conharmonic curvature tensor, concircular curvature tensor and projective curvature tensor in a Riemannian manifold. In another paper author and Mishra [2] have defined a new curvature tensor and obtained its relativistic significance.
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Curvature Tensors on Complex Lagrange Spaces
2003Let \((M,L)\) be a complex Lagrange space and let \(T_\mathbb{C} M\) be the complexification of the tangent bundle \(TM\), which is decomposed at each point of \(M\) into \(T_\mathbb{C} M=T'M+T''M\). The author expresses the local coefficients, in the adapted frame of the complex Chern-Lagrange nonlinear connection, of the Levi-Civita connection ...
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Relativity, Tensors, and Curvature
2011Heuristics of Einstein's Theory What does g00 have to do with gravitation? The Metric Potentials Einstein's general theory of relativity is primarily a replacement for Newtonian gravitation and a generalization of special relativity. It cannot be “derived”; we can only speculate, with Einstein, by heuristic reasoning, how such a generalization ...
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The length of curvature tensor for Riemannian manifold with parallel Ricci curvature tensor
Publicationes Mathematicae Debrecen, 2011In this paper, we study compact Riemannian manifolds with Þ2Ric=0, and estab- lish a pinching theorem for the square of the length of Riemannian curvature tensor. When n . 10, the pinching constant is sharp.
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On a Notion of Nonlocal Curvature Tensor
Journal of Elasticity, 2023Roberto Paroni, Brian Seguin
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On Nye’s lattice curvature tensor
Mechanics Research Communications, 2021Fabio Sozio, Arash Yavari
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