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Jee, Seo-In;Lee, Jae-Hyouk
- The Pure and Applied Mathematics
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- v.21 no.4
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- pp.257-270
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- 2014
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.
https://doi.org/10.7468/jksmeb.2014.21.4.257 인용 PDF KSCI KPUBS HTML

Lee, Kee-Young
- Communications of the Korean Mathematical Society
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- v.21 no.1
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- pp.185-191
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- 2006
This paper observes that the induced homomorphisms on cohomology groups by a cyclic map are trivial. For a CW-complex X, we use the fact to obtain some conditions of X so that the n-th Gottlieb group $G_n(X)$ is trivial for an even positive integer n. As corollaries, for any positive integer m, we obtain $G_{2m}(S^{2m})\;=\;0\;and\;G_2(CP^m)\;=\;0$ which are due to D. H. Gottlieb and G. Lang respectively, where $S^{2m}$ is the 2m- dimensional sphere and $CP^m$ is the complex projective m-space. Moreover, we show that $G_4(HP^m)\;=\;0\;and\;G_8(II)\;=\;0,\;where\;HP^m$ is the quaternionic projective m-space for any positive integer m and II is the Cayley projective space.
https://doi.org/10.4134/CKMS.2006.21.1.185 인용 PDF KSCI