In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic subman...In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li.展开更多
et Mn （n ≥ 3） be a complete Riemannian manifold with secM ≥ 1, and let Mni^ni （i = 1, 2） be two complete totally geodesic submanifolds in M. We prove that if n1 ＋ n2 = n - 2 and if the distance ｜M1M2｜≥π/2, ...et Mn （n ≥ 3） be a complete Riemannian manifold with secM ≥ 1, and let Mni^ni （i = 1, 2） be two complete totally geodesic submanifolds in M. We prove that if n1 ＋ n2 = n - 2 and if the distance ｜M1M2｜≥π/2, then Mi is isometric to s^ni/Zh, CP^m/2, or CP^ni/2/Z2 with the canonical metric when ni 〉 0, and thus, M is isometric to Sn/Zh, CPn/2, or CPn/2/Z2 except possibly iso when n = 3 and M1 （or M2） ≌ S1/Zh with h ≥ 2 or n iso= 4 and M1 （or M2） iso ≌ RP^2展开更多
Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and ...Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.展开更多
基金Research partially supported by the Ministry of Science and Environmental Protectipn of Serbia, Project 1646Research partially supported by EGIDE, Pavle Savic 07945VC(France)
文摘In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li.
文摘et Mn （n ≥ 3） be a complete Riemannian manifold with secM ≥ 1, and let Mni^ni （i = 1, 2） be two complete totally geodesic submanifolds in M. We prove that if n1 ＋ n2 = n - 2 and if the distance ｜M1M2｜≥π/2, then Mi is isometric to s^ni/Zh, CP^m/2, or CP^ni/2/Z2 with the canonical metric when ni 〉 0, and thus, M is isometric to Sn/Zh, CPn/2, or CPn/2/Z2 except possibly iso when n = 3 and M1 （or M2） ≌ S1/Zh with h ≥ 2 or n iso= 4 and M1 （or M2） iso ≌ RP^2
文摘Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.
