SILVER STRUCTURES ON THE RIEMANN EXTENSIONS

Yıl 2024, Cilt: 7 Sayı: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI" , 67 - 72 , 29.12.2024

Filiz Ocak , Şemsi Eken Meriç

https://doi.org/10.33773/jum.1567074

https://izlik.org/JA78EU76TG

Öz

In the present paper we deal with an $n-$dimensional differentiable manifold $M$ with a torsion-free linear connection $\nabla $. Here we study some properties of a silver structure on the cotangent bundle ${{T}^{*}}M$ equipped with the Riemannian extension ${{}^{R}}\nabla$ and obtain a necessary condition for which the silver semi-Riemannian manifold $\left( {{T}^{*}}M{{,}^{R}}\nabla ,S \right)$ to be a locally decomposable.

Anahtar Kelimeler

Cotangent bundle , Riemannian extension , silver structure

Kaynakça

• A. Gray, Pseudo-Riemannian Almost Product Manifolds And Submersions, J.Math. Mech. Vol.16, No.7, pp.715-737 (1967).
• S. Aslanci, S. Kazimova, A.A. Salimov, Some Remarks Concerning Riemannian Extensions, Ukrainian Math. J., Vol.62, No.5, pp.661–675 (2010).
• C. L. Bejan, S. Eken, A Characterization Of The Riemann Extension İn Terms Of Harmonicity, Czech. Math. J., Vol.67, No.1, pp.197-206 (2017).
• R. Cakan Akpinar, Some Results On Silver Riemannian Structures. Turkish Journal of Mathematics and Computer Science, Vol.14, No.1, pp.91-97(2022).
• V. Dryuma, The Riemann Extensions in Theory of Differential Equations and their Applications. Mat. Fiz., Anal., Geom., Vol.10, No.3, pp.307–325 (2003).
• F. Ocak, Some properties of the Riemannian extensions, Konuralp J. of Math., Vol.7, No.2, pp.359–362 (2019).
• F. Ocak, Some Notes on Riemannian Extensions, Balkan J. Geom. Appl., Vol.24, No.1, pp.45–50 (2019).
• M. Ozkan, B. Peltek, A New Structure On Manifolds: Silver Structure, İnternational Electronic Journal of Geometry, Vol.9, No.2, pp.59-69 (2016).
• M. Ozkan, E. Taylan, A. A. Citlak, On Lifts Of Silver Structure, Journal of Science and Arts, Vol.17, No.2, pp.223 ( 2017).
• E.M. Patterson, A.G. Walker, Riemann Extensions. Quart. J. Math. Oxford Ser., Vol.3 , pp.19–28 (1952).
• G. T. Pripoae, Classification of Semi-Riemannian Almost Product Structure, Proceeding of the Conference of Applied Differential Geometry-General Relativity and Workshop on Global Analysis, Differential Geometry and Lie Algebras, pp.243-251 (2002).
• A. Salimov, Tensor Operators and Their Applications, Nova Science Publishers, New York, (2012).
• A. A. Salimov, F. Agca, On Para-Nordenian Structures, Ann. Polon. Math, Vol.99, No.2, pp.193-200 (2010).
• A.A. Salimov, M. Iscan, F. Etayo, Paraholomorphic B-manifold and İts Properties, Topology Appl., Vol.154, pp.925-933 (2007).
• K. Yano, M. Ako, On Certain Operators Associated With Tensor Fields, Kodai Math. Sem. Rep., Vol.20, pp. 414-436 (1968).
• K. Yano, S. Ishihara, Tangent and Cotangent Bundles. Marcel Dekker, İnc., New York, (1973).
• K. Yano, M. Kon, Structures on Manifolds. Singapore: World Scientific Publishing Co., (1984).