Weyl homogeneous manifolds modeled on compact Lie groups

2009/12/30 by Nikolayevsky, Y.
#53A30 #53B20 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0912.5472

Abstract

A Riemannian manifold is called Weyl homogeneous, if its Weyl tensors at any two points are "the same", up to a positive multiple. A Weyl homogeneous manifold is modeled on a homogeneous space M₀, if its Weyl tensor at every point is "the same" as the Weyl tensor of M₀, up to a positive multiple. We prove that a Weyl homogeneous manifold Mⁿ, n ≥ 4, modeled on an irreducible symmetric space M₀ of types II or IV (compact simple Lie group with a bi-invariant metric or its noncompact dual) is conformally equivalent to M₀.

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