Complex immersions in Kähler manifolds of positive holomorphic -Ricci curvature

Authors:
Fuquan Fang and Sérgio Mendonça

Journal:
Trans. Amer. Math. Soc. **357** (2005), 3725-3738

MSC (2000):
Primary 32Q15; Secondary 53C55

DOI:
https://doi.org/10.1090/S0002-9947-05-03675-5

Published electronically:
March 25, 2005

MathSciNet review:
2146646

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Abstract | References | Similar Articles | Additional Information

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 -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 -dimensional closed manifold in a simply connected closed Kähler -manifold with positive holomorphic -Ricci curvature is an embedding, provided that . This assertion for 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:
https://doi.org/10.1090/S0002-9947-05-03675-5

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