Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1
ON THE GEOMETRY OF THE TANGENT BUNDLE WITH VERTICAL RESCALED METRIC
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 222–235
- DOI
- —
Abstract
Let (M; g) be a n-dimensional smooth Riemannian manifold. Inthe present paper, we introduce a new class of natural metrics denoted byGf and called the vertical rescaled metric on the tangent bundle TM. Wecalculate its Levi-Civita connection and Riemannian curvature tensor. Westudy the geometry of (TM; Gf) and several important results are obtainedon curvature, Einstein structure, scalar and sectional curvatures.