METALLIC STRUCTURES ON DIFFERENTIABLE MANIFOLDS


ÖZKAN M., Yilmaz F.

JOURNAL OF SCIENCE AND ARTS, no.3, pp.645-660, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2018
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.645-660
  • Keywords: Metallic ratio, metallic structure, polynomial structure, almost product structure, Riemannian manifold, metallic Riemannian manifold, GOLDEN, PROLONGATIONS
  • Gazi University Affiliated: Yes

Abstract

In this paper, we study metallic structures, i.e. polynomial structures with the structure polynomial Q(J) = J(2) - aJ -bI on manifolds using the metallic ratio, which is a generalization of the Golden proportion. We investigate for integrability and parallelism conditions of metallic structures. Also, we obtain a metallic Riemannian manifold with respect to the Riemannian metric.