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جلد 11 شماره 1 صفحات 13-26 برگشت به فهرست نسخه ها
Tangent Bundle of the Hypersurfaces in a Euclidean Space
چکیده:  

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
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 $(R^{4n},overline{J}$,$%
leftlangle ,rightrangle )$. We show that the tangent bundle $TM$ is a CR-submanifold of the Kaehler manifold  $(R^{4n},overline{J}$,$leftlangle ,rightrangle )$. 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 $(TS^{2n-1},% overline{g})$.

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نوع مطالعه: پژوهشي | موضوع مقاله: تخصصي
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DOI: 10.7508/ijmsi.2016.01.002


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Deshmukh S, Al-Shaikh S B. Tangent Bundle of the Hypersurfaces in a Euclidean Space. IJMSI. 2016; 11 (1) :13-26
URL: http://ijmsi.ir/article-1-430-fa.html
Tangent Bundle of the Hypersurfaces in a Euclidean Space. مجله علوم ریاضی و انفورماتیک ایرانیان. 1395; 11 (1) :13-26

URL: http://ijmsi.ir/article-1-430-fa.html

دوره 11، شماره 1 - ( 1-1395 ) برگشت به فهرست نسخه ها
نشریه علوم ریاضی و انفورماتیک Iranian Journal of Mathematical Sciences and Informatics
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