Variation of curvatures of subanalytic spaces and Schläfli-type formulas
type: Item
instance of: scholarly article
title: Variation of curvatures of subanalytic spaces and Schläfli-type formulas
zbMATH Open document ID: 1037.32012
DOI: 10.1023/A:1024269221528
author: Andreas Bernig
published in: Annals of Global Analysis and Geometry
publication date: 2003-08-20T00:00:00Z
review text: The aim of this paper is to prove a variational formula for Lipschitz-Killing curvatures which applies to a large class of singular spaces, namely that of subanalytic sets. The method to obtain the main result uses the normal cycle construction. This normal cycle in some sense encodes the singularities of \(X\). This construction is made by using stratified Morse theory. Then the Lipschitz-Killing invariants can be obtained by integration of some differential form over the normal cycle. As a nice consequence of this result Schläfi's formula, Hilbert's variational formula for the total scalar curvature of a manifold and the Chern-Gauss-Bonnet theorem can be put into a very general setting where these classical results can be obtained as special cases of the single variational formula proved in this paper.
Mathematics Subject Classification ID: 32C05
Mathematics Subject Classification ID: 32B20
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1968158
zbMATH Keywords: normal cycle
zbMATH Keywords: subanalytic set
zbMATH Keywords: Schläfli
zbMATH Keywords: Lipschitz-Killing curvature
zbMATH Keywords: scalar curvature
zbMATH Keywords: Einstein equation
reviewed by: Antonio Diaz-Cano
MaRDI profile type: Publication
full work available at URL: a:1024269221528
OpenAlex ID: W76135035
description: scientific article; zbMATH DE number 1968158