ISSN : 1226-0657
In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and <TEX>$S^{4n+3}$</TEX> which is invariant under <TEX>$S^3$</TEX> and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in <TEX>$S^{4n+3}$</TEX> 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.
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