Basic automorphism of Cartan foliations covered by fibrations

2020/12/08 by К. И. Шеина, Sheina, K. I.
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2012.04348

Abstract

The basic automorphism group A_B(M,F) of a Cartan foliation (M, F) is the quotient group of the automorphism group of (M, F) by the normal subgroup, which preserves every leaf invariant. For Cartan foliations covered by fibrations, we find sufficient conditions for the existence of a structure of a finite-dimensional Lie group in their basic automorphism groups. Estimates of the dimension of these groups are obtained. For some class of Cartan foliations with integrable an Ehresmann connection, a method for finding of basic automorphism groups is specified.

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