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Commun. Korean Math. Soc. 2002; 17(2): 279-293
Printed June 1, 2002
Copyright © The Korean Mathematical Society.
Kahler submanifolds with lower bounded totally real bisectional curvature tensor II
Yong-Soo Pyo, Kyoung-Hwa Shin
Pukyong National University, Pukyong National University
In this paper, we prove that if every totally real bisectional curvature of an $n(\geqq 3)$-dimensional complete K\"ahler submanifold of a complex projective space of constant holomorphic sectional curvature $c$ is greater than $\frac{c}{6n(n+1)}(3n^2 + 2n-2),$ then it is totally geodesic and compact.
Keywords: Kahler manifold, sectional curvature, holomorphic sectional curvature, totally real bisectional curvature, totally
MSC numbers: 53C50, 53C55, 53C56
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