en تخصصي Special پژوهشي Research paper <p>Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is<br> not the Riemannian submersion. In this paper, we use the fact that $R^{4n}$ is the tangent bundle of the Euclidean space $R^{2n}$ to define a special complex structure $overline{J}$ on the tangent bundle $R^{4n}$ so that $% (R^{4n},overline{J}$,$leftlangle ,rightrangle )$ is a Kaehler manifold, where $leftlangle ,rightrangle $ is the Euclidean metric which is also the Sasaki metric of the tangent bundle $R^{4n}$. We study the structure induced on the tangent bundle $(TM,overline{g})$ of the hypersurface $M$, which is a submanifold of the Kaehler manifold $(R^{4n},overline{J}$,$%<br> leftlangle ,rightrangle )$. We show that the tangent bundle $TM$ is a CR-submanifold of the Kaehler manifold&nbsp; $(R^{4n},overline{J}$,$leftlangle ,rightrangle )$. We find conditions under which certain special vector fields on the tangent bundle $(TM,overline{g})$ are Killing vector fields. It is also shown that the tangent bundle $TS^{2n-1}$ of the unit sphere $% S^{2n-1}$ admits a Riemannian metric $overline{g}$ and that there exists a nontrivial Killing vector field on the tangent bundle $(TS^{2n-1},% overline{g})$.</p> Tangent bundle, Hypersurface, Kaehler manifold, Almost contact structure, Killing vector field, CR-Submanifold, Second fundamental form, Wiengarten map. 13 26 http://ijmsi.ir/browse.php?a_code=A-10-469-1&slc_lang=en&sid=1 S. Deshmukh shariefd@ksu.edu.sa 10031947532846002915 10031947532846002915 Yes King Saud University S. B. Al-Shaikh 10031947532846002916 10031947532846002916 No King Saud University