Local Symmetry of Unit Tangent Sphere Bundle With g- Natural Almost Contact B-Metric Structure
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Abstract:
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.
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Journal title
volume 14 issue 2
pages 93- 104
publication date 2019-10
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