The index of a vector field tangent to an odd-dimensional hypersurface and the signature of the relative Hessian
type: Item
instance of: scholarly article
title: The index of a vector field tangent to an odd-dimensional hypersurface and the signature of the relative Hessian
zbMATH Open document ID: 0946.32016
DOI: 10.1007/BF02465138
author: X. Gómez-Mont
author: Pavao Mardešić
publication date: 2000-10-18T00:00:00Z
review text: The paper gives a formula for the (Poincaré-Hopf) index \(\text{Ind}_{\gamma, \pm,0}(x)\) (introduced by \textit{X. Gómez-Mont}, \textit{J. Seade} and \textit{A. Verjovsky} in Math. Ann. 291, 737-751 (1991; Zbl 0725.32012)) of a vector field \(X\) tangent to a hypersurface \(V=f^{-1}(0) \subset B\subset \mathbb{R}^{n+1}\) where \(f\) is a real-analytic function defined on the unit ball \(B\) of \(\mathbb{R}^{n+1}\) with an algebraic isolated singularity at 0.
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 32S50
Mathematics Subject Classification ID: 32S25
zbMATH DE Number: 1407609
zbMATH Keywords: singularity of holomorphic vector fields
zbMATH Keywords: Poincaré-Hopf index
zbMATH Keywords: residue mapping
reviewed by: Viorel Vâjâitu
MaRDI profile type: Publication
cites work: Q4310111
cites work: An algebraic formula for the degree of a \(C^\infty\) map germ. Sur une inegalite a la Minkowski pour les multiplicites
cites work: The index of a vector field tangent to a hypersurface and the signature of the relative Jacobian determinant
cites work: The index of a holomorphic flow with an isolated singularity
cites work: Q3322387
cites work: Q3040168
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1407609