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Homogeneous almost quaternion-Hermitian manifolds

Andrei Moroianu, Mihaela Pilca, Uwe Semmelmann

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Abstract

An almost quaternion-Hermitian structure on a Riemannian manifold is a reduction of the structure group of to . In this paper we show that a compact simply connected homogeneous almost quaternion-Hermitian manifold of non-vanishing Euler characteristic is either a Wolf space, or S-2 x S-2 , or the complex quadric SO(7)/U(3) .

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An almost quaternion-Hermitian structure on a Riemannian manifold is a reduction of the structure group of to . In this paper we show that a compact simply connected homogeneous almost quaternion-Hermitian manifold of non-vanishing Euler characteristic is either a Wolf space, or S-2 x S-2 , or the complex quadric SO(7)/U(3) .

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Available abstract

An almost quaternion-Hermitian structure on a Riemannian manifold is a reduction of the structure group of to . In this paper we show that a compact simply connected homogeneous almost quaternion-Hermitian manifold of non-vanishing Euler characteristic is either a Wolf space, or S-2 x S-2 , or the complex quadric SO(7)/U(3) .

Key concepts: Mathematics, Quaternion, Quadric, Hermitian matrix, Euler characteristic, Pure mathematics, Homogeneous, Manifold (fluid mechanics)

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