TY - JOUR
T1 - Local Symmetry of Unit Tangent Sphere Bundle With g- Natural Almost Contact B-Metric Structure
TT -
JF - IJMSI
JO - IJMSI
VL - 14
IS - 2
UR - http://ijmsi.ir/article-1-1014-en.html
Y1 - 2019
SP - 93
EP - 104
KW - Almost contact structure
KW - B-metrics
KW - g-natural metrics
KW - Local symmetry
KW - Sphere bundle.
N2 - We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ 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 G̃. More precisely, we prove that the flatness of metric g is necessary and sufficient for the g-natural metric G̃ to be locally symmetric.
M3
ER -