Negatively curved metrics on Kodaira surfaces
type: Item
instance of: scholarly article
title: Negatively curved metrics on Kodaira surfaces
zbMATH Open document ID: 0664.53033
DOI: 10.1007/BF01455062
author: I-Hsun Tsai
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164606
review text: We prove the following result. Let S be an algebraic surface admitting a Kodaira fibration over an algebraic curve C of \(genus>1\). We think of S as being a holomorphic family \(\{S_ p\}_{p\in C}\), where the \(S_ p's\) are the fibers of the fibration. To this family we can associate a holomorphic map f: \(C\to T\)- the Teichmüller space of the Riemann surface \(S_ p\). We show that S admits a Hermitian metric of negative holomorphic bisectional curvature if and only if the map f is an immersion. This implies a recent result that S has negative tangent bundle in the sense of Grauert [cf. \textit{M. Martin-Deschamps}, Ann. Inst. Fourier 39-64 (1984; Zbl 0547.14012), and \textit{M. Schneider} in Complex analysis and algebraic geometry, Proc. Conf., Göttingen 1985, Lect. Notes Math. 1194, 150-157 (1986; Zbl 0592.14016)].
reviewed by: I-Hsun Tsai
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 4086474
zbMATH Keywords: Kodaira fibration
zbMATH Keywords: Teichmüller space
zbMATH Keywords: Hermitian metric
zbMATH Keywords: Kodaira surfaces
MaRDI profile type: Publication
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OpenAlex ID: W1968682080
description: scientific article; zbMATH DE number 4086474