On the normal bundle of a complex submanifold of a locally conformal Kaehler manifold |
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Authors: | Sorin Dragomir |
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Affiliation: | (1) Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milano, Italy |
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Abstract: | We investigate the existence of parallel sections in the normal bundle of a complex submanifold of a locally conformal Kaehler manifold with positive holomorphic bisectional curvature. Also, if M is a quasi-Einstein generalized Hopf manifold then we show that any complex submanifoldM with a flat normal connection of M is quasi-Einstein, too, provided thatM is tangent to the Lee field of M. As an application of our results we study the geometry of the second fundamental form of a complex submanifold in the locally conformal Kaehler sphereQm (of a complex Hopf manifoldS2m+1 ×S1). |
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