On the Cotangent Bundle with Vertical Modified Riemannian Extensions


OCAK F.

Boletim da Sociedade Paranaense de Matematica, vol.42, 2024 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42
  • Publication Date: 2024
  • Doi Number: 10.5269/bspm.64108
  • Journal Name: Boletim da Sociedade Paranaense de Matematica
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Keywords: almost complex structure, Cotangent bundle, Golden structure, Riemannian extension
  • Karadeniz Technical University Affiliated: Yes

Abstract

Let M be an n-dimensional differentiable manifold with a torsion-free linear connection ∇ which induces on its cotangent bundle T*M. The main purpose of the present paper is to study some properties of the vertical modified Riemannian extension on T*M which is given as a new metric in [17]. At first, we investigate a metric connection with torsion on T*M. And then, we present the holomorphy properties with respect to a compatible almost complex structure. Furthermore, we study locally decomposable Golden pseudo-Riemannian structures on the cotangent bundle endowed with vertical modified Riemannian extension.