Geodesic
Index of Singularities of Real Vector Fields on Singular Hypersurfaces
Journal of Singularities, Tome 9 (2014), pp. 111-121

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Gómez-Mont, Seade and Verjovsky introduced an index, now called GSV-index, generalizing the Poincaré-Hopf index to complex vector fields tangent to singular hypersurfaces. The GSV-index extends to the real case. This is a survey paper on the joint research with Gómez-Mont and Giraldo about calculating the GSV-index of a real vector field X tangent to a singular hypersurface V=f^{-1}(0). The GSV-index is calculated as a combination of several terms. Each term is given as a signature of some bilinear form on a local algebra associated to f and X. Main ingredients in the proof are Gómez-Mont's formula for calculating the GSV-index on singular complex hypersurfaces and the formula of Eisenbud, Levine and Khimshiashvili for calculating the Poincaré-Hopf index of a singularity of a real vector field in R^{n+1}. 
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     author = {Pavao Marde\v{s}i\'c},
     title = {Index of {Singularities} of {Real} {Vector} {Fields} on {Singular} {Hypersurfaces}},
     journal = {Journal of Singularities},
     pages = {111--121},
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Pavao Mardešić. Index of Singularities of Real Vector Fields on Singular Hypersurfaces. Journal of Singularities, Tome 9 (2014), pp. 111-121. doi: 10.5427/jsing.2014.9j

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