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In this paper, tangent bundle TM of the hypersurface M in R has been studied. For hypersurface M given by immersion f : M → R, considering the fact that… Click to show full abstract
In this paper, tangent bundle TM of the hypersurface M in R has been studied. For hypersurface M given by immersion f : M → R, considering the fact that F = df : TM → R is also immersion, TM is treated as a submanifold of R. Firstly, an induced metric which is called rescaled induced metric has been defined on TM, and the Levi-Civita connection has been calculated for this metric. Next, curvature tensors of tangent bundle TM have been obtained. Finally, the orthonormal frame at the point (p, u) ∈ TM has been defined and some curvature properties of such a tangent bundle by means of orthonormal frame for a given point have been investigated.
Journal Title: TURKISH JOURNAL OF MATHEMATICS
Year Published: 2021
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