## Kyoto Journal of Mathematics

### On some aspects of duality principle

#### Abstract

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

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

Dates
Revised: 5 June 2014
Accepted: 10 June 2014
First available in Project Euclid: 9 September 2015

https://projecteuclid.org/euclid.kjm/1441824036

Digital Object Identifier
doi:10.1215/21562261-3089064

Mathematical Reviews number (MathSciNet)
MR3395978

Zentralblatt MATH identifier
06489506

#### Citation

Andrejić, Vladica; Rakić, Zoran. On some aspects of duality principle. Kyoto J. Math. 55 (2015), no. 3, 567--577. doi:10.1215/21562261-3089064. https://projecteuclid.org/euclid.kjm/1441824036

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