Abstract
LetMbe a compact3-dimensional totally umbilicalCR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector ofMdoes not vanish, thenMis either diffeomorphic toS3orRP3or a lens spaceLp,q3.
Highlights
Umbilical CR-submanifolds of a Kaehler manifold have been considered by Bejancu [2], Blair, and Chen [3]
By Hamilton’s theorem it follows that M is diffeomorphic to either S3,Rp3 or the lens space L3p, q
Summary
Umbilical CR-submanifolds of a Kaehler manifold have been considered by Bejancu [2], Blair, and Chen [3]. In this paper we consider 3-dimensional totally umbilical CR-submanifolds of a Kaehler manifold. For this case we have obtained the following theorem: Let M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature.
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