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

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

2004-11-03

arxiv.org/abs/math/0411058v1

Mathematics

Differential Geometry

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Scientific paper

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.

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