IJPAM: Volume 89, No. 1 (2013)

FOUR-DIMENSIONAL RIEMANNIAN
STANILOV-VIDEV MANIFOLDS

Maria Ivanova$^1$, Veselin Videv$^2$
Metropolitan State University of Denver
Mathematical and Computer Sciences
P.O. Box 173362, Campus Box 38, Denver, Colorado 80217-3362, USA
Department of Mathematics and Informatics
Trakia University
St. Zagora, 6000, BULGARIA


Abstract. In the present note we characterize the four-dimensional Riemannian manifolds for which any skew-symmetric Stanilov operator with respect to any plane in the tangent space to the manifold commute with the corresponding generalized Jacobi operator, at any point of the manifold. These classes of manifolds Gilkey called Stanilov-Videv manifolds.

Received: January 11, 2013

AMS Subject Classification: 53C20, 53C25

Key Words and Phrases: Riemannian manifold, Jacobi operator, skew-symmetric Stanilov operator, generalized Jacobi operator, commutative conditions, Stanilov-Videv manifold

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DOI: 10.12732/ijpam.v89i1.1 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 1