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http://dx.doi.org/10.7468/jksmeb.2014.21.4.257

ISOPARAMETRIC FUNCTIONS IN S4n+3  

Jee, Seo-In (Department of Mathematics, Ewha Womans University)
Lee, Jae-Hyouk (Department of Mathematics, Ewha Womans University)
Publication Information
The Pure and Applied Mathematics / v.21, no.4, 2014 , pp. 257-270 More about this Journal
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.
Keywords
isoparametric function; quaternionic vector space; sphere;
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