Spectrum of the Laplacian on manifolds with Spin(9) holonomy

Details Spectrum of the Laplacian on manifolds with Spin(9) holonomy Spectrum of the Laplacian on manifolds with Spin(9) holonomy

2007-11-09

arxiv.org/abs/0711.1428v2

Mathematics

Differential Geometry

24 pages

Scientific paper

We consider noncompact complete manifolds with Spin(9) holonomy and proved an one end result and a splitting type theorem under different conditions on the bottom of the spectrum. We proved that any harmonic functions with finite Dirichlet integral must be Cayley-harmonic, which allowed us to conclude an one end result. In the second part, we established a splitting type theorem by utilizing the Busemann function..

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