Pseudo-riemannian manifolds with commuting jacobi operators

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2006Embargo end date: 01 Jan 2006 English Publisher:Springer Science and Business Media LLCJournal:Rendiconti del Circolo Matematico di Palermo, volume 55, pages 163-174 (issn: 0009-725X, eissn: 1973-4409,

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Authors: Brozos-Vázquez, M.; Gilkey, P.;

doi: 10.1007/bf02874699 , 10.48550/arxiv.math/0608707

arXiv: math/0608707

Pseudo-riemannian manifolds with commuting jacobi operators

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Abstract

We study the geometry of pseudo-Riemannian manifolds which are Jacobi--Tsankov, i.e. J(x)J(y)=J(y)J(x) for all tangent vectors x and y. We also study manifolds which are 2-step Jacobi nilpotent, i.e. J(x)J(y)=0 for all tangent vectors x and y.

Related Organizations

University of Santiago de Compostela
Spain
University of Oregon
United States

Keywords

Jacobi-Tsankov manifold, Mathematics - Differential Geometry, Jacobi operators, Differential Geometry (math.DG), FOS: Mathematics, 53C20, Global Riemannian geometry, including pinching

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