Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 55, Number 3 (2015), 567-577.
On some aspects of duality principle
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.
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
Permanent link to this document
Digital Object Identifier
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.)
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