کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4606138 | 1337684 | 2013 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Minimal unit vector fields with respect to Riemannian natural metrics
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let (M,g) be a Riemannian manifold. We denote by GË an arbitrary Riemannian g-natural metric on the unit tangent sphere bundle T1M, such metric depends on four real parameters satisfying some inequalities. The Sasaki metric, the Cheeger-Gromoll metric and the Kaluza-Klein metrics are special Riemannian g-natural metrics. In literature, minimal unit vector fields have been already investigated, considering T1M equipped with the Sasaki metric GËS [12]. In this paper we extend such characterization to an arbitrary Riemannian g-natural metric GË. In particular, the minimality condition with respect to the Sasaki metric GËS is invariant under a two-parameters deformation of the Sasaki metric. Moreover, we show that a minimal unit vector field (with respect to GË) corresponds to a minimal submanifold. Then, we give examples of minimal unit vector fields (with respect to GË). In particular, we get that the Hopf vector fields of the unit sphere, the Reeb vector field of a K-contact manifold, and the Hopf vector field of a quasi-umbilical hypersurface with constant principal curvatures in a Kähler manifold, are minimal unit vector fields (with respect to GË).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 31, Issue 6, December 2013, Pages 820-835
Journal: Differential Geometry and its Applications - Volume 31, Issue 6, December 2013, Pages 820-835
نویسندگان
Domenico Perrone,