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