Original Article
Kyungpook Mathematical Journal 2003; 43(1): 37-48
Published online March 23, 2003
Copyright © Kyungpook Mathematical Journal.
Semi-invariant Submanifolds with $L$-flat Normal Connection in terms of the Lie Derivatives
U-Hang Ki1, Chunji Li2, Seong-Cheol Lee3
1Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea
2Department of Mathematics, Yanbian University, Yanji 133-002, P. R. China
2Topology and Geometry Research Center, Kyungpook National University, Taegu 702-701, Korea
3Department of Mathematics, Chosun University, Kwangju 502-759, Korea
We study a semi-invariant submanifold of codimention 3 with $L$-flat normal connection in a complex projective space, and classify the submanifold above satisfying $L_{xi}A=0$ or $L_{xi}S=0$, where $A, S$ and $L_{xi}$ denote by the shape operator in the direction of the
distinguished normal, the Ricci tensor of the submanifold and the operator of the Lie derivative with respect to the structure vector $xi$ respectively.
Keywords: semi-invariant submanifold, distinguished normal, L- at normal connection, Lie derivative