Some Properties of the Riemannian Extensions

Abstract

In this article, we construct an almost complex structure on the cotangent bundle. Then we investigate Nordenian properties of  the  Riemannian extension  in the cotangent bundle.

Keywords

• Riemannian extension,cotangent bundle,almost complex structure

References

1. [1] S. Aslanci, S. Kazimova and A.A. Salimov, Some notes concerning Riemannian extensions, Ukrainian Math. J., 62 (2010), 661-675.
2. [2] A. Bonome, R. Castro, L. M. Hervella and Y. Matsushita, Construction of Norden structures on neutral 4-manifolds, JP J. Geom. Topol., 5 (2005), 121-140.
3. [3] S.L. Drut¸˘a, Classes of general natural almost anti-Hermitian structures on the cotangent bundles, Mediterranean J. Math, 8 (2011), 161-179.
4. [4] G.T. Ganchev and A.V. Borisov, Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulg. Sci.,39(1986), 31–34.
5. [5] M. Iscan, A.A. Salimov, On K¨ahler-Norden manifolds, Proc. Indian Acad. Sci. Math. Sci., 119(2009), 71-80.
6. [6] G.I. Kruckovic, Hypercomplex structures on manifolds.I, Trudy. Sem. Vektor. Tenzor. Anal., 16(1972), 174-201(in Russian).
7. [7] A. Salimov, Tensor Operators and Their Applications, Nova Science Publishers, New York, 2012.
8. [8] A.A. Salimov, M. Iscan and K. Akbulut, Some remarks concerning hyperholomorphic B-manifolds, Chin. Ann. Math., 29(2008), 631–640.

9. [9] A.A. Salimov, M. Iscan and F. Etayo, Paraholomorphic B-manifold and its properties, Topology Appl., 154(2007), 925-933.
10. [10] A.A. Salimov, S. Turanli, Curvature properties of anti-K¨ahler-Codazzi manifolds, C. R. Acad. Sci. Paris, Ser. I, 351(2013), 225–227.
11. [11] V.V. Vishnevskii, Integrable affinor structures and their plural interpretations, J. Math. Sci., 108(2002), 151-187.
12. [12] K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Pure and Applied Mathematics, 16, Marcel Dekker, Inc., New York, 1973.