REAL HYPERSUREAACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH PARALLEL SHAPE OPERATOR II

Title & Authors
REAL HYPERSUREAACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH PARALLEL SHAPE OPERATOR II
Suh, Young-Jin;

Abstract
In this paper we consider the notion of ξ-invariant or (equation omitted)-invariant real hypersurfaces in a complex two-plane Grassmannian $\small{G_2}$( $\small{C^{m+2}}$) and prove that there do not exist such kinds of real hypersurfaces in $\small{G_2}$( $\small{C^{m+2}}$) with parallel second fundamental tensor on a distribution ζ defined by ζ = ξ U(equation omitted), where(equation omitted) = Span ｛ξ$\small{_1}$, ξ$\small{_2}$, ξ$\small{_3}$｝.X>｝.
Keywords
complex Grassmannians;real hypersurfaces;tubes;shape operator;Kahler structure;quaternionic Kahler structure.;
Language
English
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11.
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15.
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16.
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References
1.
Funct. Anal. Appl., 1968. vol.2. pp.106-114

2.
J. Reine Angew. Math., 1991. vol.419. pp.9-26

3.
Rend. Sem. Mat. Univ. Politec Torino, 1991. vol.55. pp.19-83

4.
Monatsh. Math, 1999. vol.127. pp.1-14

5.
Monatsh. Math., 2002. vol.137. pp.87-98

6.
Trans. Amer. Math. Soc., 1982. vol.269. pp.481-499

7.
Trans. Amer. Math. Soc., 1986. vol.296. pp.137-149

8.
Tsukuba J. Math., 1991. vol.15. pp.547-561

9.
J. Geom., 1994. vol.49. pp.166-177

10.
Diff. Geom. Appl., 1997. vol.7. pp.211-217

11.
Bull. Austral. Math. Soc., 2003. vol.67. pp.493-502

12.
Bull. Austral. Math. Soc., 2003. vol.68. pp.379-393