The horizontal heat kernel on the quaternionic anti de-Sitter spaces and related twistor spaces

TL;DR

This paper investigates the geometry of quaternionic anti-de Sitter spaces, deriving explicit formulas for the horizontal Laplacian and heat kernel, and explores related twistor spaces and their heat kernels, connecting to the quaternionic magnetic Laplacian.

Contribution

It provides explicit formulas for the horizontal Laplacian and heat kernel on quaternionic anti-de Sitter spaces and analyzes related twistor spaces and their heat kernels.

Findings

Derived explicit heat kernel formulas for quaternionic anti-de Sitter spaces

Analyzed small time asymptotics of the heat kernel

Explored connections to quaternionic magnetic Laplacian

Abstract

The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel formula is explicit enough to derive small time asymptotics. Related twistor spaces and corresponding heat kernels are also discussed and the connection to the quaternionic magnetic Laplacian is done.