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Moduli space of branched superminimal immersions of a compact Riemann surface into S4

Part of: Global differential geometry Holomorphic fiber spaces Spaces and manifolds of mappings Classical differential geometry Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  09 April 2009

Bonaventure Loo
Bonaventure Loo
Affiliation:
Department of Mathematics Lower Kent Ridge Road, National Univesity of Singapore, Singapore, 119260 e-mail: bloo@math.nus.edu.sg
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Abstract

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In this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S4. We prove that when d ≥ max {2g, g + 2}, such spaces have the structure of projectivzed fibre products and are path-connected quasi projective varieties of dimension 2d − g + 4. This generalizes known results for spaces of harmonic 2-spheres in S4.

MSC classification

Secondary: 58D27: Moduli problems for differential geometric structures 58E20: Harmonic maps , etc. 53A10: Minimal surfaces, surfaces with prescribed mean curvature 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 32L25: Twistor theory, double fibrations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 1 , February 1999 , pp. 32 - 50
Copyright
Copyright © Australian Mathematical Society 1999

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