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HARMONIC MORPHISMS AND SUBMANIFOLDS WITH CONFORMAL SECOND FUNDAMENTAL FORMS

Published online by Cambridge University Press:  01 May 2003

XIAOHUAN MO
XIAOHUAN MO
Affiliation:
LMAM School of Mathematical Sciences, Peking University, Beijing 100871, China e-mail: moxh@pku.edu.cn
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Abstract

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We show that surfaces such that the natural projections of the unit normal bundles are harmonic morphisms are composed of minimal points and totally umbilical points. As its application, we find a harmonic map from the torus to the complex quadric in $CP^3$ such that the projection map of the associated sphere bundle constructed by Gudmundsson is not a harmonic morphism. This contrasts sharply with the situation for holomorphic maps. We also establish sufficient conditions for reducing the codimension of an isometric immersion with conformal second fundamental form.

Keywords

53C1253C4358E20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 143 - 151
Copyright
2003 Glasgow Mathematical Journal Trust

Footnotes

This work is supported by the National Natural Science Foundation of China 10171002.