Potential Analysis

, Volume 41, Issue 3, pp 959–982

The Subelliptic Heat Kernels of the Quaternionic Hopf Fibration

Article

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.

Keywords

Heat kernel Quaternionic Hopf fibration Small-time asymptotics 

Mathematics Subject Classifications

58J35 53C17 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsPurdue University West LafayetteWest LafayetteUSA

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