The subelliptic heat kernels of the quaternionic Hopf fibration

2013/10/22 by Fabrice Baudoin, Jing Wang, Baudoin, Fabrice +1 · 2 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1310.5938

Abstract

The main goal of this work is to study the sub-Laplacian of the unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the quaternionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of the conformal sub-Laplacian and small-time asymptotics. As a byproduct of our study we also obtain several results related to the sub-Laplacian of a projected Hopf fibration.

Cited by

• Quaternionic stochastic areas on quaternionic full flag manifolds and applications
• The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries

Related

• The subelliptic heat kernel of the octonionic Hopf fibration
• The horizontal heat kernel on the quaternionic anti de-Sitter spaces and related twistor spaces
• Integral representation of the subelliptic heat kernel on the complex anti-de Sitter fibration
• The Subelliptic Heat Kernel on the CR sphere
• Heat kernel asymptotics for quaternionic contact manifolds