On the Cotangent Bundle with Vertical Modified Riemannian Extensions
Boletim da Sociedade Paranaense de Matematica, vol.42, 2024 (ESCI, Scopus)
- 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.