Geodesic
On the geometry of tangent bundles with a class of metrics
Esmaeil Peyghan1 ; Abbas Heydari2 ; Leila Nourmohammadi Far1
1Department of Mathematics Faculty of Science Arak University Arak 38156-8-8349, Iran
2Department of Mathematics Tarbiat Modares University Tehran, Iran
Annales Polonici Mathematici, Tome 103 (2012) no. 3, pp. 229-246
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We introduce a class of metrics on the tangent bundle of a Riemannian manifold and find the Levi-Civita connections of these metrics. Then by using the Levi-Civita connection, we study the conformal vector fields on the tangent bundle of the Riemannian manifold. Finally, we obtain some relations between the flatness (resp. local symmetry) properties of the tangent bundle and the flatness (resp. local symmetry) on the base manifold.
DOI : 10.4064/ap103-3-2
Keywords: introduce class metrics tangent bundle riemannian manifold levi civita connections these metrics using levi civita connection study conformal vector fields tangent bundle riemannian manifold finally obtain relations between flatness resp local symmetry properties tangent bundle flatness resp local symmetry base manifold

Esmaeil Peyghan  1   ; Abbas Heydari  2   ; Leila Nourmohammadi Far  1

1 Department of Mathematics Faculty of Science Arak University Arak 38156-8-8349, Iran
2 Department of Mathematics Tarbiat Modares University Tehran, Iran 
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Esmaeil Peyghan; Abbas Heydari; Leila Nourmohammadi Far. On the geometry of tangent bundles with a class of metrics. Annales Polonici Mathematici, Tome 103 (2012) no. 3, pp. 229-246. doi: 10.4064/ap103-3-2

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