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The index of a vector field tangent to an odd-dimensional hypersurface and the signature of the relative Hessian. (English. Russian original) Zbl 0946.32016
Funct. Anal. Appl. 33, No. 1, 1-10 (1999); translation from Funkts. Anal. Prilozh. 33, No. 1, 1-13 (1999).
The paper gives a formula for the (Poincaré-Hopf) index \(\text{Ind}_{\gamma, \pm,0}(x)\) (introduced by X. Gómez-Mont, J. Seade and 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.

32S65 Singularities of holomorphic vector fields and foliations
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
32S25 Complex surface and hypersurface singularities
Full Text: DOI
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