J. Korean Math. Soc. 2004; 41(3): 535-565
Printed May 1, 2004
Copyright © The Korean Mathematical Society.
Young Jin Suh
Kyungpook National University
In this paper we consider the notion of $\xi$-invariant or ${\frak D}^{\bot}$-invariant real hypersurfaces in a complex two-plane Grassmannian $G_2({\Bbb C}^{m+2})$ and prove that there do not exist such kinds of real hypersurfaces in $G_2({\Bbb C}^{m+2})$ with parallel second fundamental tensor on a distribution $\frak F$ defined by ${\frak F}={\xi}\cup{\frak D}^{\bot}$, where ${\frak D}^{\bot}=\text{Span}\ \{{\xi}_1,{\xi}_2,{\xi}_3\}$.
Keywords: complex Grassmannians, real hypersurfaces, tubes, shape operator, Kahler structure, quaternionic Kahler structure
MSC numbers: Primary 53C40; Secondary 53C15
2015; 52(6): 1337-1346
2004; 41(5): 795-808
2007; 44(1): 211-235
2007; 44(3): 647-659
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd