Isoparametric submanifolds
Abstract
In this talk we consider two classes of submanifolds in Euclidean spaces that are characterized by simple local invariants. The first class consists of submanifolds with costant principal curvatures. These are by definition submanifolds 
such that for every parallel normal vector field 
along a curve in the eigenvalues of the shape operator 
are constant, see [St] and [0l2]. The second class of submanifolds we will consider consists of isoparametric submainfolds. These are by definition submanifolds such that the normal bundle is flat and the eigenvalues of the shape operator 
are constant for every locally defined parallel normal vector field 
, see [Ha], [CW], [Te] and [PT 2]. It is of course clear that isoparametric submanifolds have constant principal curvatures.
such that for every parallel normal vector field along a curve in the eigenvalues of the shape operator are constant, see [St] and [0l2]. The second class of submanifolds we will consider consists of isoparametric submainfolds. These are by definition submanifolds such that the normal bundle is flat and the eigenvalues of the shape operator are constant for every locally defined parallel normal vector field , see [Ha], [CW], [Te] and [PT 2]. It is of course clear that isoparametric submanifolds have constant principal curvatures.DOI Code:
10.1285/i15900932v9supp33
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