Harmonicity of horizontally conformal maps and spectrum of the Laplacian

Gabjin Yun

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 30, 1-7

Abstract:

We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that if Φ : M → N is a horizontally conformal map such that the tension field is divergence free, then Φ is harmonic. Furthermore, if N is noncompact, then Φ must be constant. Also we show that the projection of a warped product manifold onto the first component is harmonic if and only if the warping function is constant. Finally, we describe a characterization for a horizontally conformal map with a constant dilation preserving an eigenfunction.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:394068

DOI: 10.1155/S0161171202107058

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