An integral formula for the heat kernel of tubular neighborhoods of complete (connected) Riemannian manifolds
type: Item
instance of: scholarly article
title: An integral formula for the heat kernel of tubular neighborhoods of complete (connected) Riemannian manifolds
zbMATH Open document ID: 0862.58052
published in: Potential Analysis
publication date: 1997-05-25T00:00:00Z
review text: The author considers a complete Riemannian manifold \(M\) and a submanifold \(N\) with its normal bundle. Using Fermi coordinates with respect to \(N\) he obtains an integral formula for the Dirichlet heat kernel and so a probabilistic representation for the integral \(\int_N f(y) p^{M_0}_t (x,y)dy\) where \(f\) is any measurable function with compact support on \(M_0\), a tubular neighbourhood on \(N\), and \(p\) is the above heat kernel. This allows the author to obtain heat kernel formulae for the complex projective space \(\mathbb{C} P^n\), the quaternionic projective space \(QP^n\) and the Caley line \(CaP^1\).
reviewed by: Yuri E. Gliklikh
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 936750
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: Fermi coordinates
zbMATH Keywords: heat kernel
zbMATH Keywords: complex projective space
zbMATH Keywords: quaternionic projective space
zbMATH Keywords: Caley line
author: Martin Ngu Ndumu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 936750