für Mathematik in den Naturwissenschaften Leipzig Examples of signature ( 2 , 2 ) manifolds with commuting curvature operators
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چکیده
We exhibit Walker manifolds of signature (2, 2) with various commutativity properties for the Ricci operator, the skew-symmetric curvature operator, and the Jacobi operator. If the Walker metric is a Riemannian extension of an underlying affine structure A, these properties are related to the Ricci tensor of A.
منابع مشابه
für Mathematik in den Naturwissenschaften Leipzig Dually Flat Manifolds and Global Information Geometry
Dually flat manifolds constitute fundamental mathematical objects of information geometry. This note establishes some facts on the global properties and topology of dually flat manifolds which, in particular, provide answers to questions and problems in global information geometry posed by Amari and Amari-Nagaoka.
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