• 대한수학회보
• /
• 제19권1호
• /
• pp.1-7
• /
• 1982

• 대한수학회지
• /
• 제17권2호
• /
• pp.175-192
• /
• 1981

• Kyungpook Mathematical Journal
• /
• 제24권2호
• /
• pp.115-125
• /
• 1984

• Kyungpook Mathematical Journal
• /
• 제25권1호
• /
• pp.15-28
• /
• 1985

• 대한수학회논문집
• /
• 제2권1호
• /
• pp.89-115
• /
• 1987

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제21권4호
• /
• pp.257-270
• /
• 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.

• Kyungpook Mathematical Journal
• /
• 제45권3호
• /
• pp.363-394
• /
• 2005

In this expository paper we survey basic results on isotropic immersions.

• 대한수학회논문집
• /
• 제21권1호
• /
• pp.185-191
• /
• 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.