The asymptotics of heat kernels on Riemannian foliations
type: Item
instance of: scholarly article
title: The asymptotics of heat kernels on Riemannian foliations
zbMATH Open document ID: 0911.58040
author: D. Massart
published in: Geometric and Functional Analysis. GAFA
publication date: 1999-04-22T00:00:00Z
review text: Let \(M\) be an \(n\)-dimensional, connected, oriented Riemannian manifold. Assume that \(M\) is equipped with a Riemannian foliation \(\mathcal F\) of dimension \(q\). In the paper under review, the basic Laplacian of the foliation is compared with the induced Laplacian on the basic manifold. The author shows how to express an asymptotic expansion (of Minaksasundaram-Plejfel type) of the basic heat kernel on functions as \(t \rightarrow 0\), in terms of geometric invariants of the foliations. The result is generalized to the other transversally elliptic operators acting on the space of basic sections of a vector bundle, such as the basic Laplacian on \(k\)-forms and the square of a basic Dirac operator.
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 53C12
zbMATH DE Number: 1156784
zbMATH Keywords: basic Laplacian
zbMATH Keywords: heat kernel
zbMATH Keywords: Riemannian foliation
zbMATH Keywords: Dirac operator
reviewed by: Novica Blažić
MaRDI profile type: Publication
full work available at URL: s000390050060
OpenAlex ID: W2065072165
Wikidata QID: Q115389253
DOI: 10.1007/S000390050060
description: scientific article; zbMATH DE number 1156784