ISOPARAMETRIC FUNCTIONS IN S^(4n+3)
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In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and S^(4n+3) which is invariant under S^3 and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in S^(4n+3) with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.
Abstract
In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and S^(4n+3) which is invariant under S^3 and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in S^(4n+3) with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.
참고문헌 (16)
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