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Invariants over Curvature Tensor Fields

โœ Scribed by Xiaoping Xu

Book ID
102576121
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
293 KB
Volume
202
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

In this paper, we present constructions of higher-order polynomial O n -invariants over curvature tensor fields. These invariants are higher-order analogues of the scalar curvature. Our methods are based on certain replicative properties of ลฝ . the O n -module structure on a ''curvature space'' and a realization of a ''curva-ลฝ . ture space'' by the action of the symmetric tensor of the Lie algebra so n on symmetric matrices. By our methods, we are able to find a complete generator set of functional invariants over the curvature tensor fields of a manifold with lower dimensions.

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