The Euler characteristic of hypersurfaces in space forms and applications to isoparametric hypersurfaces

Abstract

We revisit Allendoerfer-Weil's formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, first taking some time to re-prove it while demonstrating techniques of [2] and then applying it to gain new understanding of isoparametric hypersurfaces.

arXiv commentNew formulation of Theorem 7.5 and a new remark before Theorem 7.6; accepted for publication in the Pacific Journal of Mathematics; article started in Portugal, announced in Spain, finished in China and published in California, USA. The author dedicates this work to the commemorations of the 500th anniversary of the first global circumnavigation voyage by the Portuguese and Spanish navigators

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