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

Rui Albuquerque

Vol. 312 (2021), No. 2, 259–277

DOI: 10.2140/pjm.2021.312.257

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