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Volume :8 Issue : 1 1981      Add To Cart                                                                    Download

Generalised conformal mappings

Auther : A. SVEC

Department of Mathematics, University of Kuwait

 

ABSTRACT

 

In the first part of the paper, we investigate the differential equation ∆w =hw for I-forms M. on a compact Riemannian 2-manifold M, h being a given function. As an application, we produce a theorem for vanishing vector fields on M generalising infinitesimally conformal fields on one hand and harmonic fields on the other hand. In the last section, we study the general equation ∆f = ل (f) on the unit sphere with a special emphasis on the case ل (f) = 1-eëf . The geometrical application is then provided by exhibiting metrics conformal to the standard metric of S2 (1) m, the Gauss curvature of which satisfies a certain condition.

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Jun 19, 2012

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