The spectral geometry of the canonical Riemannian submersion of a compact Lie Group

Details The spectral geometry of the canonical Riemannian submersion of a compact Lie Group The spectral geometry of the canonical Riemannian submersion of a compact Lie Group

2006-10-26

arxiv.org/abs/math/0610788v1

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.geomphys.2007.05.002

Let G be a compact connected Lie group which is equipped with a bi-invariant Riemannian metric. Let m(x,y)=xy be the multiplication operator. We show the associated fibration m mapping GxG to G is a Riemannian submersion with totally geodesic fibers and we study the spectral geometry of this submersion. We show the pull back of eigenforms on the base have finite Fourier series on the total space and we give examples where arbitrarily many Fourier coefficients can be non-zero. We give necessary and sufficient conditions that the pull back of a form on the base is harmonic on the total space.

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