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arXiv · 1804.04680

Smoothness Conditions in Cohomogeneity manifolds

Luigi Verdiani·Wolfgang Ziller
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Abstract

In this paper we discuss the smoothness conditions for metrics on a cohomogeneity one manifold, i.e. metrics invariant under a Lie group whose generic orbits are hypersurfaces. Along these hypersurfaces one describes the metrics in terms of a collection of functions defined along a geodesic normal to the hypersurfaces. In a neighborhood of a lower dimensional orbit the functions must satisfy certain smoothness conditions for the metric to extend smoothly. In general these can be quite complicated. We present a method that makes it straightforward to compute them, and illustrate it in several examples. This second version contains some improvements in exposition and a reformulation of Theorem B, with a proof added.

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Luigi Verdiani, Wolfgang Ziller. 2020-08-11. Smoothness Conditions in Cohomogeneity manifolds. https://arxiv.org/abs/1804.04680

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