Restrictions on harmonic morphisms
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- by M. T. Mustafa
- Conform. Geom. Dyn. 3 (1999), 102-115
- DOI: https://doi.org/10.1090/S1088-4173-99-00026-0
- Published electronically: August 16, 1999
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Abstract:
We consider horizontally (weakly) conformal maps $\phi$ between Riemannian manifolds and calculate a formula for the Laplacian of the dilation of $\phi$, 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.References
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Bibliographic 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
- Received by editor(s): December 29, 1997
- Received by editor(s) in revised form: June 8, 1999
- Published electronically: August 16, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Conform. Geom. Dyn. 3 (1999), 102-115
- MSC (1991): Primary 58E20, 53C20
- DOI: https://doi.org/10.1090/S1088-4173-99-00026-0
- MathSciNet review: 1716571