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

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