Vol. 312, No. 2, 2021

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

Rui Albuquerque

Vol. 312 (2021), No. 2, 259–277
Abstract

We revisit the Allendoerfer–Weil formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, taking time to re-prove it while demonstrating techniques of (Albuquerque 2019a) and then applying it to gain new understanding of isoparametric hypersurfaces.

Keywords
Euler characteristic, hypersurface, mean curvatures, space form, isoparametric hypersurface
Mathematical Subject Classification
Primary: 53C35, 57R20
Secondary: 53C17, 58A15
Milestones
Received: 21 January 2020
Revised: 28 March 2021
Accepted: 9 April 2021
Published: 31 August 2021
Authors
Rui Albuquerque
Universidade de Évora
Évora
Portugal