On the geometry of tangent bundles with a class of metrics

Esmaeil Peyghan, Abbas Heydari, and Leila Nourmohammadi Far. "On the geometry of tangent bundles with a class of metrics." Annales Polonici Mathematici 103.3 (2012): 229-246. <http://eudml.org/doc/280569>.

@article{EsmaeilPeyghan2012,
abstract = {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.},
author = {Esmaeil Peyghan, Abbas Heydari, Leila Nourmohammadi Far},
journal = {Annales Polonici Mathematici},
keywords = {conformal vector field; fiber-preserving; homothetic; Killing vector field; locally symmetric; totally geodesic},
language = {eng},
number = {3},
pages = {229-246},
title = {On the geometry of tangent bundles with a class of metrics},
url = {http://eudml.org/doc/280569},
volume = {103},
year = {2012},
}

TY - JOUR
AU - Esmaeil Peyghan
AU - Abbas Heydari
AU - Leila Nourmohammadi Far
TI - On the geometry of tangent bundles with a class of metrics
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 3
SP - 229
EP - 246
AB - 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.
LA - eng
KW - conformal vector field; fiber-preserving; homothetic; Killing vector field; locally symmetric; totally geodesic
UR - http://eudml.org/doc/280569
ER -