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arXiv · 1706.08489

Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations

Fabrice Baudoin·Erlend Grong·Kazumasa Kuwada·Anton Thalmaier
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Abstract

We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian foliations, we show that sharp horizontal and vertical comparison theorems for the sub-Riemannian distance may be obtained as a limit of horizontal and vertical comparison theorems for the Riemannian distances approximations.

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Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada, Anton Thalmaier. 2017-06-26. Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations. https://arxiv.org/abs/1706.08489

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