The index of a vector field tangent to an odd-dimensional hypersurface and the signature of the relative Hessian
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.
singularity of holomorphic vector fields
scientific article; zbMATH DE number 1407609