A New Class of Golden Riemannian Manifold

In this paper, we introduce a new class of almost Golden Riemannian structures and study their essential examples as well as their fundamental properties. Next, we investigate a particular type belonging to this class and we establish some basic results for Riemannian curvature tensor and the sectional curvature. Concrete examples are given.

___

  • [1] Beldjilali, G.: Induced Structures on Golden Riemannian Manifolds. Beitr Algebra Geom. 59 (4), 761-777 (2018).
  • [2] Beldjilali, G.: s-Golden manifolds, Mediterr. J. Math. (2019). https://doi.org/10.1007/s00009-019-1343-9.
  • [3] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics, Vol. 203, Birhauser, Boston, (2002).
  • [4] Boyer, C.P., Galicki, K., Matzeu, P.: On Eta-Einstein Sasakian Geometry. Comm.Math. Phys. 262, 177-208 (2006).
  • [5] Crasmareanu, M., Hretecanu C.E.: Golden differential geometry. Chaos, Solitons & Fractals. 38, 1124-1146 (2008).
  • [6] Etayo, F., Santamaria R., Upadhyay, A.: On the Geometry of Almost Golden Riemannian Manifolds, Mediterr. J. Math. 14,14-187 (2017). doi 10.1007/s00009-017-0991-x.
  • [7] Gezer, A., Cengiz N., Salimov, A.: On integrability of Golden Riemannian structures. Turkish J.Math. 37, 693-703 (2013).
  • [8] Gezer, A., Karaman, C.: Golden-Hessian Structures. Proc. Nat. Acad. Sci. 86, 41-46 (2016).
  • [9] Hretcanu, C. E.: Submanifolds in Riemannian manifold with Golden structure. In: Workshop on Finsler Geometry and its Applications, Hungary (2007).
  • [10] Ozkan, M., Yilmaz, F.: Prolongation of Golden structures to tangent bundles of order r. Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. Volume 65 (1), 35-47 (2016).
  • [11] Sahin, B., Akyol, M. A.: Golden maps between Golden Riemannian manifolds and constancy of certain maps. Math. Commun. 19, 333-342 (2014).
  • [12] Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Math., Vol 3, World Sci., (1984).