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A BOCHNER TECHNIQUE FOR HARMONIC MORPHISMS

Published online by Cambridge University Press:  01 June 1998

M. T. MUSTAFA
M. T. MUSTAFA
Affiliation:
Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi, Distt. Swabi, NWFP, Pakistan. E-mail: [email protected]
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Abstract

We establish a Weitzenböck formula for harmonic morphisms between Riemannian manifolds and show that under suitable curvature conditions, such a map is totally geodesic. As an application of the Weitzenböck formula we obtain some non-existence results of a global nature for harmonic morphisms and totally geodesic horizontally conformal maps between compact Riemannian manifolds. In particular, it is shown that the only harmonic morphisms from a Riemannian symmetric space of compact type to a compact Riemann surface of genus at least 1 are the constant maps.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 746 - 756
Copyright
The London Mathematical Society 1998

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