Singular Values of Riemann Curvature Tensor
Xiaokai He, Hua Xiang
TL;DR
This paper introduces the concept of singular values for the Riemann curvature tensor, exploring their properties and relationships to invariants like the Ricci scalar in the context of general relativity.
Contribution
It is the first to define and analyze the singular values of the Riemann curvature tensor, linking them to classical invariants in differential geometry.
Findings
Singular values relate to Ricci scalar and other invariants.
Properties of singular values are characterized for typical cases.
The concept provides new insights into the structure of the curvature tensor.
Abstract
We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties related to the singular values, and investigate five typical cases to show its relationship to the Ricci scalar and other invariants.
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Taxonomy
TopicsTensor decomposition and applications · Black Holes and Theoretical Physics · Elasticity and Material Modeling