Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 095, 13 pages      arXiv:0708.0957      http://dx.doi.org/10.3842/SIGMA.2007.095
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Stanilov-Tsankov-Videv Theory

Miguel Brozos-Vázquez a, Bernd Fiedler b, Eduardo García-Río a, Peter Gilkey c, Stana Nikcevic d, Grozio Stanilov e, Yulian Tsankov e, Ramón Vázquez-Lorenzo a and 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

Received August 07, 2007, in final form September 22, 2007; Published online September 28, 2007

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.

Key words: 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.

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