Miguel Brozos-Vázquez, Bernd Fiedler, Eduardo García-Río, Peter Gilkey, Stana Nikčević, Grozio Stanilov, Yulian Tsankov, Ramón Vázquez-Lorenzo, Veselin Videv, “Stanilov–Tsankov–Videv Theory”, SIGMA, 2007, Volume 3,095, 13 pp.

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SIGMA, 2007 Volume 3, 095, 13 pp. (Mi sigma221)

This article is cited in 12 papers

Stanilov–Tsankov–Videv Theory

Miguel Brozos-Vázquez^a, Bernd Fiedler^b, Eduardo García-Río^a, Peter Gilkey^c, Stana Nikčević^d, Grozio Stanilov^e, Yulian Tsankov^e, Ramón Vázquez-Lorenzo^a, Veselin Videv^f

^a Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
^b Eichelbaumstr. 13, D-04249 Leipzig, Germany
^c Mathematics Department, University of Oregon, Eugene Oregon 97403-1222, USA
^d Mathematical Institute, SANU, Knez Mihailova 35, p.p. 367, 11001 Belgrade, Serbia
^e Sofia University "St. Kl. Ohridski", Sofia, Bulgaria
^f Mathematics Department, Thracian University, University Campus, 6000 Stara Zagora, Bulgaria

Abstract: We survey some recent results concerning Stanilov–Tsankov–Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold.

Keywords: algebraic curvature tensor; anti-self-dual; conformal Jacobi operator; conformal Osserman manifold; Jacobi operator; Jacobi–Tsankov; Jacobi–Videv; mixed-Tsankov; Osserman manifold; Ricci operator; self-dual; skew-symmetric curvature operator; skew-Tsankov; skew-Videv; Walker manifold; Weyl conformal curvature operator.

MSC: 53B20

Received: August 7, 2007; in final form September 22, 2007; Published online September 28, 2007

Language: English

DOI: 10.3842/SIGMA.2007.095

Bibliographic databases:

ArXiv: 0708.0957

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