Displaying similar documents to “Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature.”

The spectral geometry of the Weyl conformal tensor

N. Blažić, P. Gilkey, S. Nikčević, U. Simon (2005)

Banach Center Publications

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We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the skew-symmetric curvature operator defined by the Weyl conformal curvature tensor.

The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor

Mileva Prvanović (2013)

Communications in Mathematics

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By using the technique of decomposition of a Hermitian vector space under the action of a unitary group, Ganchev [2] obtained a tensor which he named the Weyl component of the antiholomorphic curvature tensor. We show that the same tensor can be obtained by direct application of the conformal change of the metric to the antiholomorphic curvature tensor. Also, we find some other conformally curvature tensors and examine some relations between them.

Spinor equations in Weyl geometry

Buchholz, Volker

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This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with C -spin structures. A conformal Schrödinger-Lichnerowicz formula is presented and used to derive integrability conditions for these equations. It is shown that the only non-closed Weyl manifolds of dimension greater than 3 that admit solutions of the real Killing equation are 4-dimensional and non-compact. Any Weyl manifold of dimension greater than 3, that admits a real Killing spinor has to be Einstein-Weyl. ...