Intersections of quadrics with spheres

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Author(s) : Tsasa Lusala

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 678-2000

MSC 2000

53A15 Affine differential geometry

Abstract :
In Euclidean space $\R^{n+2}$ we study the intersections of central quadrics with spheres where we consider the intersections as hypersurfaces in $\S^{n+1}(1)$. It is our aim to characterize such intersections within the class of all hypersurfaces in $\S^{n+1}(1)$ with Weingarten operator of maximal rank. The methods we use are similar to methods from affine hypersurface theory.

Keywords : Quadrics, polar pairs, isoparametric hypersurfaces