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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.

First Page

2008

Last Page

2024

Included in

Mathematics Commons

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