Abstract

MARIN ARANGO, Carlos Alberto  and  BLAZQUEZ-SANZ, David. Infinitesinally homogeneous manifolds with prescribed structure groups. Rev.colomb.mat. [online]. 2016, vol.50, n.1, pp.1-15. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v50n1.62175.

Abstract We explore the class of triples (M, ∇, P) where M is a manifold, ∇ is an afine 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 ⊆ 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.

Keywords : homogeneous manifold; Inner torsion; G-structures.

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