Turkish Journal of Mathematics
DOI
10.3906/mat-2102-52
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.
Keywords
Tangent bundle, hypersurface, rescaled induced metric, curvature tensor, orthonormal frame
First Page
2008
Last Page
2024
Recommended Citation
YURTTANÇIKMAZ, SEMRA
(2021)
"On the geometry of tangent bundle of a hypersurface in $%%TCIMACRO{\U{211d} }%%BeginExpansion\mathbb{R}%EndExpansion^{n+1}$,"
Turkish Journal of Mathematics: Vol. 45:
No.
5, Article 9.
https://doi.org/10.3906/mat-2102-52
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss5/9
