A Bochner Technique for Harmonic Morphisms |
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Authors: | Mustafa M T |
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Institution: | Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology Topi, Distt. Swabi, NWFP, Pakistan. E-mail: mustafa{at}giki.sdnpk.undp.org |
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Abstract: | We establish a Weitzenböck formula for harmonic morphismsbetween Riemannian manifolds and show that under suitable curvatureconditions, such a map is totally geodesic. As an applicationof the Weitzenböck formula we obtain some non-existenceresults of a global nature for harmonic morphisms and totallygeodesic horizontally conformal maps between compact Riemannianmanifolds. In particular, it is shown that the only harmonicmorphisms from a Riemannian symmetric space of compact typeto a compact Riemann surface of genus at least 1 are the constantmaps. |
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