Some Results On Silver Riemannian Structures

Abstract

Our aim in this paper is to study of silver Riemannian structures on manifold and bundle. An integrability condition and curvature properties for silver Riemannian structure are investigated via the Tachibana operator. Twin silver Riemannian metric is defined and some properties of twin silver Riemannian metric are investigated. Examples of silver structure are given on tangent and cotangent bundles.

Keywords

• Silver structure
• pure tensor
• Riemannian manifold
• twin metric

References

1. Çayır, H., Operators on metallic Riemannian structures, Honam Math. J., 42(1)(2020), 63-74.
2. Gezer, A., Karaman, Ç., On metallic Riemannian structures, Turk. J. Math., 39(6)(2015), 954-962.
3. Hretcanu, C., Crasmareanu, M., Metallic structures on Riemannian manifolds, Rev. Un. Mat. Argentina, 54 (2013), 15-27.
4. Iscan, M., Salimov A.A., On Kahler-Norden manifolds, Proc. Indian Acad. Sci., 119(1)(2009), 71-80.
5. Ocak, F., Notes on the Sasaki metrics in cotangent bundles, Comp.Ren.Bul.Ac., 72(7)(2019), 871-879.
6. Ozkan, M., Peltek, B., A new structure on manifolds:Silver structure, Int Electron J Geom., 9(2)(2016), 59-69.
7. Salimov, A.A., Akbulut, K., Aslanci, S., A note on integrability of almost product Riemannian structures, Arab. J. Sci. Eng. Sect. A Sci., 34(1)(2009), 153-157.
8. Salimov, A.A., Agca, F., Some Properties of Sasakian Metrics in Cotangent Bundles, Mediterr. J. Math., 8(2) (2011), 243-255.

9. Salimov, A.A., Tensor Operators and Their applications. Nova Science Publ. New York, (2013).
10. Spinadel, V.W., The metallic means family and multifractal spectra. Nonlinear Anal. Ser. B: Real World Appl., 36(6)(1999), 721-745.
11. Spinadel, V.W., The metallic means family and forbidden symmetries, Int. Math. J., 2(3)(2002), 279-288.
12. Tachibana, S., Analytic tensor and its generalization, Tohoku Math J., 12(1968), 208-221.
13. Yano K., Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, New York, (1965).
14. Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, New York, (1973).