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Kähler metrics of negative holomorphic bisectional curvature on Kodaira surfaces
Author(s) -
To WingKeung,
Yeung SaiKee
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq117
Subject(s) - fibration , holomorphic function , curvature , mathematics , metric (unit) , pure mathematics , riemann surface , space (punctuation) , mathematical analysis , topology (electrical circuits) , geometry , combinatorics , computer science , homotopy , operations management , economics , operating system
We construct a Kähler metric of negative holomorphic bisectional curvature on any compact complex surface that admits a Kodaira fibration. This is achieved by considering the curvature of the Weil–Petersson metric on an associated Teichmüller space of punctured Riemann surfaces.