Harmonicity of horizontally conformal maps and spectrum of the Laplacian. (2002)

• Record Type: Journal Article
• Authors: Yun, Gabjin
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 30:Number 12(2002)
• Page Start: 709
• Page End: 715
• Publication Date: 2002
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171202107058
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : We discuss the harmonicity of horizontally conformal maps and their relations with the spectrum of the Laplacian. We prove that ifΦ : M → N is a horizontally conformal map such that the tension field is divergence free, thenΦ is harmonic. Furthermore, ifN is noncompact, thenΦ 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.