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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Complex immersions in Kähler manifolds of positive holomorphic $k$-Ricci curvature


Authors: Fuquan Fang and Sérgio Mendonça
Journal: Trans. Amer. Math. Soc. 357 (2005), 3725-3738
MSC (2000): Primary 32Q15; Secondary 53C55
Published electronically: March 25, 2005
MathSciNet review: 2146646
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Abstract: The main purpose of this paper is to prove several connectedness theorems for complex immersions of closed manifolds in Kähler manifolds with positive holomorphic $k$-Ricci curvature. In particular this generalizes the classical Lefschetz hyperplane section theorem for projective varieties. As an immediate geometric application we prove that a complex immersion of an $n$-dimensional closed manifold in a simply connected closed Kähler $m$-manifold $M$ with positive holomorphic $k$-Ricci curvature is an embedding, provided that $2n\ge m+k$. This assertion for $k=1$ follows from the Fulton-Hansen theorem (1979).


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Additional Information

Fuquan Fang
Affiliation: Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Email: fuquanfang@eyou.com

Sérgio Mendonça
Affiliation: DepartamentodeAnálise,\hskip1mm Universidade FederalFluminense (UFF), Niterói, 24020-140 RJ Brazil
Email: sxmendonca@hotmail.com, mendonca@mat.uff.br

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03675-5
PII: S 0002-9947(05)03675-5
Received by editor(s): August 5, 2003
Received by editor(s) in revised form: March 10, 2004
Published electronically: March 25, 2005
Additional Notes: The first author was supported by NSFC Grant 19741002, RFDP and the Qiu-Shi Foundation
Article copyright: © Copyright 2005 American Mathematical Society