On the Structure of Equidistant Foliations of Euclidean Space

Details On the Structure of Equidistant Foliations of Euclidean Space On the Structure of Equidistant Foliations of Euclidean Space

2007-12-03

arxiv.org/abs/0712.0245v1

Mathematics

Differential Geometry

PhD thesis at University of Augsburg, Germany (Advisor: Ernst Heintze); slightly revised version; 56 pages, 8 figures

Scientific paper

This thesis is concerned with equidistant foliations of Euclidean space, i.e. partitions into complete, connected, properly embedded smooth submanifolds. The space of leaves is an Alexandrov space of nonnegative curvature and the canonical projection is a submetry. Generalizing a result of Gromoll and Walschap we show that an equidistant foliation always has an affine leaf and we prove homogeneneity of the foliation under certain additional assumptions. Moreover, we give several reducibility results and construct new (noncompact) inhomogeneous examples of equidistant foliations.

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