On the Geometry of the Curvature Operators Defined by Stanilov

Authors:

Pages: 25-30
DOI: https://doi.org/10.54664/BOVE9277

Abstract:

In the presented article, we consider the curvature operators defined by Stanilov and derive results related to one of them. A main problem in studying Riemannian manifolds with the indicated curvature operators is a condition for point constancy of the eigenvalues of these operators, as an extension of Osserman’s conjecture for point constancy of the Jacobi operator. The results of Stanilov, Gilkey, Videv, and their co-authors are directed in this area, and a condition for commutativity of these operators was also introduced. These studies have been the subject of several dissertations and monographs and of numerous articles, as well.

Keywords:

Stanilov operators, Jacobi operator, pointwise constant Osserman manifolds.

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