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Existence of the Ehresmann connection on a manifold foliated by the locally free action of a commutative Lie group

Research paper by P. N. Ivanshin

Indexed on: 03 Nov '04Published on: 03 Nov '04Published in: Mathematics - Differential Geometry



Abstract

In this paper the author determines necessary and sufficient conditions for existence of the Ehresmann connection on a manifold foliated by locally free action of the commutative Lie group. Also here we describe structure of $C_0(M)|_L$ for a leaf $L \subset M$ in case such a connection exists. Finally we give some results on structure of the spectrum of the family of Schr\"odinger operators related to the leaves of the foliation.