Infinitesimally homogeneous manifolds with prescribed structure groups
Differential Geometry
2016-02-15 v1
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.
Cite
@article{arxiv.1602.03923,
title = {Infinitesimally homogeneous manifolds with prescribed structure groups},
author = {Carlos Alberto Marín Arango and David Blázquez-Sanz},
journal= {arXiv preprint arXiv:1602.03923},
year = {2016}
}
Comments
9 pages