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arXiv · 1602.03923

Infinitesimally homogeneous manifolds with prescribed structure groups

Carlos Alberto Marín Arango·David Blázquez-Sanz
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Abstract

We explore the class of triples (M, nabla, P) where M is a manifold, nabla is an affine connection in M and P is a G-structure in M. Inside this class there are infinitesimally homogeneous manifolds, characterized by having G-constant curvature, torsion and inner torsion. For each matrix Lie group G subgroup of GL(Rn) there is a class of infinitesimally homogeneous manifolds with structure group G. In this paper we characterize the classes of infinitesimally homogeneous manifolds for some specific values of the structure group G including: identity group, finite groups, diagonal group, special linear group, orthogonal group and unitary group.

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Carlos Alberto Marín Arango, David Blázquez-Sanz. 2016-02-11. Infinitesimally homogeneous manifolds with prescribed structure groups. https://arxiv.org/abs/1602.03923

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