Transverse Weitzenb\'ock formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves

Autor:	Baudoin, Fabrice, Kim, Bumsik, Wang, Jing
Rok vydání:	2014
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We prove a family of new Weitzenb\"ock formulas on a Riemannian foliation with totally geodesic leaves. These Weitzenb\"ock formulas are naturally parametrized by the canonical variation of the metric. As a consequence, under natural geometric conditions, the horizontal Laplacian satisfies a generalized curvature dimension inequality. Among other things, this curvature dimension inequality implies Li-Yau estimates for positive solutions of the horizontal heat equation and a sub-Riemannian Bonnet-Myers compactness theorem whose assumptions only rely on the intrinsic geometry of the horizontal distribution. Comment: To be published in Communications in Analysis and Geometry
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1408.0548 Zobrazit plný text záznamu View this record from Arxiv