f(a,b)(3,2,1)-structures on manifolds


GÖK M. , KILIÇ E., Özgür C.

Journal of Geometry and Physics, vol.169, 2021 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 169
  • Publication Date: 2021
  • Doi Number: 10.1016/j.geomphys.2021.104346
  • Title of Journal : Journal of Geometry and Physics
  • Keywords: Almost quadratic ϕ-structure, Metallic pseudo-Riemannian structure, Polynomial structure, ϵ-framed metric structure

Abstract

© 2021 Elsevier B.V.In this paper, we define and study two new structures on a differentiable manifold called by us an f(a,b)(3,2,1)-structure and a framed f(a,b)(3,2,1)-structure as a generalization of some geometric structures determined by polynomial structures, where a,b∈R and b≠0. At beginning, we present some examples regarding f(a,b)(3,2,1)-structures and establish their some fundamental properties. We also give a necessary condition for an f(a,b)(3,2,1)-structure to be an almost quadratic ϕ-structure. Later, it is shown that the existence of two semi-Riemannian metrics on differentiable manifolds admitting a framed f(a,b)(3,2,1)-structure, i.e., framed f(a,b)(3,2,1)-manifolds. In particular, a framed f(a,b)(3,2,1)-manifold endowed with the first semi-Riemannian metric mentioned above is called a framed metric f(a,b)(3,2,1)-manifold. Finally, we construct some examples to illustrate the existence of framed metric f(a,b)(3,2,1)-manifolds.