Curvature and Gauss-Bonnet defect of global affine hypersurfaces

Details Curvature and Gauss-Bonnet defect of global affine hypersurfaces Curvature and Gauss-Bonnet defect of global affine hypersurfaces

2004-07-05

arxiv.org/abs/math/0407056v2

Bull Sci Math, 130 (2006), no.2, 110--122.

Mathematics

Differential Geometry

15 p., some changes in editing

Scientific paper

10.1016/j.bulsci.2005.08.003

The total curvature of complex hypersurfaces in $\bC^{n+1}$ and its variation
in families appear to depend not only on singularities but also on the
behaviour in the neighbourhood of infinity. We find the asymptotic loss of
total curvature towards infinity and we express the total curvature and the
Gauss-Bonnet defect in terms of singularities and tangencies at infinity.

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