NDLI: Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Content Provider	Springer Nature Link
Author	Králové, Hradec Dušek, Zdeněk
Copyright Year	2015
Abstract	Let (M, g) be a 4-dimensional Einstein Riemannian manifold. At each point p of M, the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p. In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O(4) acts as a transformation group between ST bases at T p M and for the so-called 2-stein curvature tensors, the group Sp(1) ⊂ SO(4) acts as a transformation group between ST bases. In the present work, the complete list of Lie subgroups of SO(4) which act as transformation groups between ST bases for certain classes of Einstein curvature tensors is presented. Special representations of groups SO(2), T 2, Sp(1) or U(2) are obtained and the classes of curvature tensors whose transformation group into new ST bases is one of the mentioned groups are determined.
Ending Page	1115
Page Count	15
Starting Page	1101
File Format	PDF
ISSN	00114642
e-ISSN	15729141
Journal	Czechoslovak Mathematical Journal
Issue Number	4
Volume Number	65
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-01-10
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Singer-Thorpe basis Ordinary Differential Equations Analysis Convex and Discrete Geometry 2-stein manifold Mathematics Special Riemannian manifolds (Einstein, Sasakian, etc.) Mathematical Modeling and Industrial Mathematics Einstein manifold
Content Type	Text
Resource Type	Article
Subject	Mathematics

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