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Minimal immersions of S2 and ℝP2 into ℂPn with few higher order singularities

Published online by Cambridge University Press:  24 October 2008

J. Bolton ,
L. M. Woodward  and
L. Vrancken
J. Bolton
Affiliation:
Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE
L. M. Woodward
Affiliation:
Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE
L. Vrancken
Affiliation:
Department Wiskunde, Katholieke Universiteit Lenven, Celestijnenlaan 2008, B3001 Lenven, Belgium
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Extract

In this paper we extend ideas developed in 2, 4 to study certain minimal immersions of S2 and ℝP2 into ℂPn. Here S2 denotes the unit sphere in ℝ3 with its standard conformal structure and ℝP2 is S2 factored out by the antipodal map, while ℂPn denotes complex projective n-space equipped with the FubiniStudy metric of constant holomorphic sectional curvature 4. Since ℝPn with its standard metric of constant curvature 1 is included in ℂPn as a totally geodesic submanifold, this includes the case of minimal immersions into the unit sphere Sn(1) with its standard metric.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 1 , January 1992 , pp. 93 - 101
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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