On the geometry of the tangent bundle with vertical rescaled generalized Cheeger- Gromoll metric

On the geometry of the tangent bundle with vertical rescaled generalized Cheeger- Gromoll metric

Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G f and called the vertical rescaled generalized Cheeger-Gromoll metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature t...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Bulletin of the Transilvania University of Braşov: Series III Mathematics & Computer Science 2020-01, Vol.12 (2), p.247-264
Hauptverfasser: Belarbi, L., El hendi, H., Letti, F.
Format: Artikel
Sprache:eng
Schlagworte:
Riemann manifold
Tensors
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Let (M, g) be an n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G f and called the vertical rescaled generalized Cheeger-Gromoll metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature tensor. We study the geometry of (TM, G f ).
ISSN:2810-2029
2065-2151
DOI:10.31926/but.mif.2019.12.61.2.5