Author/Authors :
Firuzi, Farshad Department of Mathematics - Payame Noor University, Tehran, Iran , Alipour Fakhri, Yousef Department of Mathematics - Payame Noor University, Tehran, Iran , Peyghan, Esmaeil Department of Mathematics - Faculty of Science - Arak University, Arak, Iran
Abstract :
We consider the unit tangent sphere bundle of Riemannian
manifold (M, g) with g-natural metric ˜G and we equip it to an almost
contact B-metric structure. Considering this structure, we show that
there is a direct correlation between the Riemannian curvature tensor of
(M, g) and local symmetry property of ˜G. More precisely, we prove that
the flatness of metric g is necessary and sufficient for the g-natural metric
˜G
to be locally symmetric.
