ON ANTI-INVARIANT MAXIMAL SPACELIKE SUBMANIFOLDS OF AN INDEFINITE COMPLEX SPACE FORM Page No: 1429-1432

Augustus Nzomo Wali

Keywords: Anti-invariant submanifold, Spacelike submanifold, Complex space form, totally geodesic.

Abstract: The purpose of this paper is to study the geometry of an n-dimensional anti-invariant maximal spacelike submanifold M immersed in a 2(n+p)-dimensional indefinite complex space form M(c),c ?0 of holomorphic sectional curvature c and index 2p and give a pinching result of the Ricci and scalar curvatures of M. We have shown that if the Ricci curvature R is less than ( ) ( )( ) ( ) 1 2 1 4 2 4 1 c n n n p n p ? + + ? ??? ? + + ? ??? then M is totally geodesic. Moreover the scalar curvature ( ) ( )( ) ( ) 1 2 1 4 2 4 1 c n n n n p n p ? ? + + ? ? ??? ? + + ? ??? and if ? is less than ( ) ( )( ) ( ) 1 2 1 4 2 4 1 c n n n n p n p ? + + ? ??? ? + + ? ??? them M is totally geodesic.



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