Curvature and Gauss-Bonnet defect of global affine hypersurfaces

Dirk Siersma; Mihai Tibar

doi:10.1016/j.bulsci.2005.08.003

Curvature and Gauss-Bonnet defect of global affine hypersurfaces

Differential Geometry 2007-05-23 v2 Algebraic Geometry Complex Variables

Authors: Dirk Siersma , Mihai Tibar

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Abstract

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.

Keywords

complex hypersurfaces total curvature Gauss-Bonnet defect singularities at infinity asymptotic loss

Cite

@article{arxiv.math/0407056,
  title  = {Curvature and Gauss-Bonnet defect of global affine hypersurfaces},
  author = {Dirk Siersma and Mihai Tibar},
  journal= {arXiv preprint arXiv:math/0407056},
  year   = {2007}
}

Comments

15 p., some changes in editing

Curvature and Gauss-Bonnet defect of global affine hypersurfaces

Abstract

Keywords

Cite

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