A deformation in families of Hodge-de Rham theory
type: Item
instance of: scholarly article
title: A deformation in families of Hodge-de Rham theory
zbMATH Open document ID: 1058.58009
author: Jean-Michel Bismut
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-08-20T00:00:00Z
review text: This paper reports a deformation of the Levi-Civita superconnection associated to a family of de Rham-Hodge operators, whose curvature is a family of second order hypoelliptic operators along the fibers of the cotangent bundle of the given fibration. Two identities about the square of superconnection and the hypoelliptic Laplacian on cotangent bundle is announced respectively.
reviewed by: Na Jisheng
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58H15
Mathematics Subject Classification ID: 58A99
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 55R99
zbMATH DE Number: 2093941
zbMATH Keywords: Levi-Civita superconnection
zbMATH Keywords: de Rham-Hodge operator
zbMATH Keywords: curvature
zbMATH Keywords: hypoelliptic operator
MaRDI profile type: Publication
full work available at URL: j.crma.2004.01.010
OpenAlex ID: W2050026145
cites work: The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
cites work: The hypoelliptic Laplacian on the cotangent bundle.
cites work: A deformation of Hodge theory on the cotangent bundle
cites work: Flat Vector Bundles, Direct Images and Higher Real Analytic Torsion
DOI: 10.1016/J.CRMA.2004.01.010
description: scientific article; zbMATH DE number 2093941