[en] 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.
Disciplines :
Mathematics
Author, co-author :
Baudoin, Fabrice; Department of Mathematics > University of Connecticut, USA
Grong, Erlend; LSS-SUPÉLEC > Université Paris-Sud, France
Kuwada, Kazumasa; Department of Mathematics, Graduate School of Science > Tohoku University, Japan
THALMAIER, Anton ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations
Publication date :
August 2019
Journal title :
Calculus of Variations and Partial Differential Equations
