scholarly journals About the value distribution of holomorphic maps into the projective space

1969 ◽  
Vol 123 (0) ◽  
pp. 83-114 ◽  
Author(s):  
Wilhelm Stoll
Keyword(s):  
Projective Space ◽  
Value Distribution ◽  
Holomorphic Maps

A Big Picard Theorem for Holomorphic Maps into Complex Projective Space

2009 ◽  
Vol 52 (1) ◽  
pp. 154-160
Author(s):  
Yasheng Ye ◽  
Min Ru
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Holomorphic Maps ◽  
Analytic Subvariety ◽  
Picard Theorem ◽  
Complex Projective

AbstractWe prove a big Picard type extension theoremfor holomorphic maps f : X–A → M, where X is a complex manifold, A is an analytic subvariety of X, and M is the complement of the union of a set of hyperplanes in ℙn but is not necessarily hyperbolically imbedded in ℙn.

Harmonic maps from surfaces into pseudo-Riemannian spheres and hyperbolic spaces

1983 ◽  
Vol 94 (3) ◽  
pp. 483-494 ◽  
Author(s):  
S. Erdem
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Hyperbolic Spaces ◽  
Euclidean Sphere ◽  
Holomorphic Maps ◽  
Space Forms ◽  
Indefinite Metrics ◽  
Complex Hyperbolic Spaces ◽  
Complex Projective

In [2, 4, 5, 6, 7] Calabi, Barbosa and Chern showedthat there is a 2:1 correspondence between arbitrary pairs of full isotropic (terminology as in [8]) harmonic maps ±φ:M→S2mfrom a Riemann surface to a Euclidean sphere and full totally isotropic holomorphic maps f:M→2mfrom the surface to complex projective space. In this paper we show, very explicitly, how to construct a similar one-to-one correspondence whenS2mis replaced by some other space forms of positive and negative curvatures with their standard (indefinite) metrics obtained by restricting a standard (indefinite) bilinear form on Euclidean space to the tangent spaces. We get over a difficulty encountered by Barbosa of dealing with the zeros of a certain wedge product by a technique adapted from [8]. The case of complex projective space forms (indefinite complex projective and complex hyperbolic spaces) will be considered in a separate paper. Some further developments in classification theorems are given by Eells and Wood [8], Rawnsley[14], [15] and Erdem and Wood [10].

Sign in / Sign up

Export Citation Format

Share Document