Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 4,  2011, pp.395-410
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.4.395
Title & Authors
Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator
Jeong, Im-Soon; Suh, Young-Jin;

Abstract
In this paper we give a non-existence theorem for Hopf hypersurfaces M in complex two-plane Grassmannians $\small{G_2(\mathbb{C}^{m+2})}$ whose normal Jacobi operator $\small{\bar{R}_N}$ is parallel on the distribution F defined by $\small{F=[{\xi}]{\cup}D^{\bot}}$, where [$\small{{\xi}}$] = Span{$\small{{\xi}}$}, $\small{D^{\bot}}$ = Span {$\small{{\xi}_1}$, $\small{{\xi}_2}$, $\small{{\xi}_3}$} and $\small{T_xM=D{\oplus}D^{\bot}}$, $\small{x{\in}M}$.
Keywords
Real hypersurfaces;Complex two-plane Grassmannians;F-parallel normal Jacobi operator;Hopf hypersurfaces;
Language
English
Cited by
1.
Commuting structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians, Acta Mathematica Sinica, English Series, 2015, 31, 1, 111
2.
Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians, Monatshefte für Mathematik, 2013, 172, 2, 167
3.
Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians, Czechoslovak Mathematical Journal, 2015, 65, 2, 569
4.
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator, Czechoslovak Mathematical Journal, 2015, 65, 1, 207
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