Turkish Journal of Mathematics
Abstract
In this paper, tangent bundle $TM$ of the hypersurface $M$ in $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1}$ has been studied. For hypersurface $M$ given by immersion $f:M\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n+1},$ considering the fact that $F=df:TM\rightarrow %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}$ is also immersion, $TM$ is treated as a submanifold of $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2n+2}.$ 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 $(p,u)\in TM$ has been defined and some curvature properties of such a tangent bundle by means of orthonormal frame for a given point have been investigated.
DOI
10.3906/mat-2102-52
Keywords
Tangent bundle, hypersurface, rescaled induced metric, curvature tensor, orthonormal frame
First Page
2008
Last Page
2024
Recommended Citation
YURTTANÇIKMAZ, S (2021). On the geometry of tangent bundle of a hypersurface in $%%TCIMACRO{\U{211d} }%%BeginExpansion\mathbb{R}%EndExpansion^{n+1}$. Turkish Journal of Mathematics 45 (5): 2008-2024. https://doi.org/10.3906/mat-2102-52
