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Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations. (arXiv:1706.08489v1 [math.DG])
来源于:arXiv
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. 查看全文>>