## Journal of Mathematics of Kyoto University

### On parabolic geometry of type PGL(d,C)/P

Indranil Biswas

#### Abstract

Let $P$ be the maximal parabolic subgroup of $\text{PGL}(d, {\mathbb C})$ defined by invertible matrices $(a_{ij})_{i,j=1}^d$ with $a_{dj}\,=\, 0$ for all $j\, \in\, [1\, ,d-1]$. Take a holomorphic parabolic geometry $(M\, ,E_P\, ,\omega)$ of type $\text{PGL}(d,{\mathbb C})/P$. Assume that $M$ is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map $f\, :\, {\mathbb C} {\mathbb P}^1\,\longrightarrow \, M$, then $M$ is biholomorphic to the projective space ${\mathbb C}{\mathbb P}^{d-1}$.

#### Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 4 (2008), 747-755.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250271316

Digital Object Identifier
doi:10.1215/kjm/1250271316

Mathematical Reviews number (MathSciNet)
MR2513584

Zentralblatt MATH identifier
1175.53039

#### Citation

Biswas, Indranil. On parabolic geometry of type PGL(d,C)/P. J. Math. Kyoto Univ. 48 (2008), no. 4, 747--755. doi:10.1215/kjm/1250271316. https://projecteuclid.org/euclid.kjm/1250271316