The aim of this paper is to generalize the construction of an Ambrose-Singer connection for Riemannian homogeneous manifolds to the case of cohomogeneity one Riemannian manifolds. Necessary and sufficient conditions are given on a Riemannian manifold (M,g) in order that there exists a Lie group of isometries acting on M with principal orbits of codimension one.
A canonical connection for Lie group actions / F. PODESTA'. - In: RESULTS IN MATHEMATICS. - ISSN 1422-6383. - STAMPA. - 27:(1995), pp. 105-112. [10.1007/BF03322274]
A canonical connection for Lie group actions
PODESTA', FABIO
1995
Abstract
The aim of this paper is to generalize the construction of an Ambrose-Singer connection for Riemannian homogeneous manifolds to the case of cohomogeneity one Riemannian manifolds. Necessary and sufficient conditions are given on a Riemannian manifold (M,g) in order that there exists a Lie group of isometries acting on M with principal orbits of codimension one.
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