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  • P-ISSN3059-0604
  • E-ISSN3059-1309
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ISSN : 3059-0604

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Vol.21 No.4

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ISOPARAMETRIC FUNCTIONS IN S^(4n+3)

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2014, v.21 no.4, pp.257-270
https://doi.org/10.7468/jksmeb.2014.21.4.257
Jee, Seo-In
Lee, Jae-Hyouk
Jee,, S. , & Lee,, J. (2014). ISOPARAMETRIC FUNCTIONS IN S^(4n+3), 21(4), 257-270, https://doi.org/10.7468/jksmeb.2014.21.4.257

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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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

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