Restrictions on harmonic morphisms

Author:
M. T. Mustafa

Journal:
Conform. Geom. Dyn. **3** (1999), 102-115

MSC (1991):
Primary 58E20, 53C20

DOI:
https://doi.org/10.1090/S1088-4173-99-00026-0

Published electronically:
August 16, 1999

MathSciNet review:
1716571

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider horizontally (weakly) conformal maps between Riemannian manifolds and calculate a formula for the Laplacian of the dilation of , using the language of moving frames. Applying this formula to harmonic horizontally (weakly) conformal maps or equivalently to harmonic morphisms we obtain a Weitzenböck formula similar to an earlier result of the author (J. London Math. Soc. (2) **57** (1998), 746-756), and hence vanishing results for harmonic morphisms from compact manifolds of positive curvature. Further, a method is developed to obtain restrictions on harmonic morphisms from some *non-compact* and *non-positively curved* domains. Finally, a discussion of restrictions on harmonic morphisms between simply connected space forms is given.

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Additional Information

**M. T. Mustafa**

Affiliation:
Assistant Professor, Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi, Distt. Swabi, N.W.F.P., Pakistan

Email:
mustafa@giki.edu.pk

DOI:
https://doi.org/10.1090/S1088-4173-99-00026-0

Keywords:
Harmonic morphisms,
harmonic maps,
Bochner technique

Received by editor(s):
December 29, 1997

Received by editor(s) in revised form:
June 8, 1999

Published electronically:
August 16, 1999

Article copyright:
© Copyright 1999
American Mathematical Society