Kyoto Journal of Mathematics

On some aspects of duality principle

Vladica Andrejić and Zoran Rakić

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This paper is devoted to the study of the relation between Osserman algebraic curvature tensors and algebraic curvature tensors which satisfy the duality principle. We give a short overview of the duality principle in Osserman manifolds and extend this notion to null vectors. Here, it is proved that a Lorentzian totally Jacobi-dual curvature tensor is a real space form. Also, we find out that a Clifford curvature tensor is Jacobi-dual. We provide a few examples of Osserman manifolds which are totally Jacobi-dual and an example of an Osserman manifold which is not totally Jacobi-dual.

Article information

Kyoto J. Math., Volume 55, Number 3 (2015), 567-577.

Received: 11 October 2013
Revised: 5 June 2014
Accepted: 10 June 2014
First available in Project Euclid: 9 September 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics
Secondary: 53B30: Lorentz metrics, indefinite metrics 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Duality principle Osserman manifold Clifford structure


Andrejić, Vladica; Rakić, Zoran. On some aspects of duality principle. Kyoto J. Math. 55 (2015), no. 3, 567--577. doi:10.1215/21562261-3089064.

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