Volume 14, Issue 2 (10-2019)                   IJMSI 2019, 14(2): 93-104 | Back to browse issues page

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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.

Type of Study: Research paper | Subject: General