Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 IN A COMPLEX HYPERBOLIC SPACE

  • KI, U-HANG (Dept. of Mathematics, Kyungpook National University) ;
  • LEE, SEONG-BAEK (Dept. of Mathematics, Chosun University) ;
  • LEE, AN-AYE (Dept. of Software development, Dong Shin University)
  • Received : 2001.02.19
  • Published : 2001.07.30
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Abstract

In this paper we prove the following : Let M be a semi-invariant submanifold with almost contact metric structure (${\phi}$, ${\xi}$, g) of codimension 3 in a complex hyperbolic space $H_{n+1}{\mathbb{C}}$. Suppose that the third fundamental form n satisfies $dn=2{\theta}{\omega}$ for a certain scalar ${\theta}({\leq}{\frac{c}{2}})$, where ${\omega}(X,\;Y)=g(X,\;{\phi}Y)$ for any vectors X and Y on M. Then M has constant eigenvalues correponding the shape operator A in the direction of the distinguished normal and the structure vector ${\xi}$ is an eigenvector of A if and only if M is locally congruent to one of the type $A_0$, $A_1$, $A_2$ or B in $H_n{\mathbb{C}}$.

Keywords

References

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