Skip to Main Content

Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Restrictions on harmonic morphisms
HTML articles powered by AMS MathViewer

by M. T. Mustafa
Conform. Geom. Dyn. 3 (1999), 102-115
Published electronically: August 16, 1999


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.
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (1991): 58E20, 53C20
  • Retrieve articles in all journals with MSC (1991): 58E20, 53C20
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:
  • 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:
  • MathSciNet review: 1716571