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Second variation and Legendrian stabilities of minimal Legendrian submanifolds in Sasakian manifolds
Hajime Ono 《Differential Geometry and its Applications》2005,22(3):327-340
First, we derive a new second variation formula which holds for minimal Legendrian submanifolds in Sasakian manifolds. Using this, we prove that any minimal Legendrian submanifold in an η-Einstein Sasakian manifold with “nonpositive” η-Ricci constant is stable. Next we introduce the notion of the Legendrian stability of minimal Legendrian submanifolds in Sasakian manifolds. Using our second variation formula, we find a general criterion for the Legendrian stability of minimal Legendrian submanifolds in η-Einstein Sasakian manifolds with “positive” η-Ricci constant. 相似文献
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Yong-Geun Oh 《Inventiones Mathematicae》1990,101(1):501-519
Research at MSRI supported in part by NSF Grant DMS-8505550 相似文献
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Legendrian submanifolds in Sasakian space forms play an important role in contact geometry. Defever et al. (Boll Unione Mat Ital B 7(11):365–374, 1997) established the first Chen inequality for C-totally real submanifolds in Sasakian space forms. In this article, we improve this first Chen inequality for Legendrian submanifolds in Sasakian space forms. 相似文献
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Hông-Vân Lê 《Differential Geometry and its Applications》2004,21(3):297-316
In this note we study the moduli space of minimal Legendrian submanifolds in the standard sphere S2n−1. We show that new examples of minimal Legendrian submanifolds can be constructed, if we can solve a certain equation for a function on a nearby glued Legendrian submanifold. As a step toward solving this equation, we prove short-time existence for a particular gradient flow on the space of immersed Legendrian submanifolds. A new necessary condition for a Lagrangian embedding into is given. 相似文献
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Masahiro Kon 《Mathematische Annalen》1976,219(3):277-290
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The purpose of this paper is to initiate a study of the differential geometry of lightlike (degenerate) submanifolds of semi-Riemannian manifolds. We construct the transversal vector bundle for an arbitrary lightlike submanifold and obtain results on the geometric structures induced on it. 相似文献
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Second variation of harmonic maps between Finsler manifolds 总被引:3,自引:0,他引:3
SHEN Yibing & ZHANG YanDepartment of Mathematics Zhejiang University Hangzhou China Correspondence should be addressed to Shen Yibing 《中国科学A辑(英文版)》2004,47(1):39-51
The first and second variation formulas of the energy functional for a nonde-generate map between Finsler manifolds is derived. As an application, some nonexistence theorems of nonconstant stable harmonic maps from a Finsler manifold to a Riemannian manifold are given. 相似文献
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Two-dimensional submanifolds of four-dimensional manifolds 总被引:2,自引:0,他引:2
V. A. Rokhlin 《Functional Analysis and Its Applications》1971,5(1):39-48
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Sorin Dragomir 《Israel Journal of Mathematics》1988,61(2):199-210
The main results we obtain are as follows: an invariant submanifold of a Hopf manifold with semi-flat normal connection is
either a complex hypersurface or a totally-umbilical quasi-Einstein submanifold with a flat normal connection. The only totally-umbilical
invariant submanifolds of zero scalar curvature of a Hopf manifold are the totally-geodesic flat surfaces.
To Professor A. Cossu on the Occasion of his 65th Birthday 相似文献
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Manfio Fernando Roth Julien Upadhyay Abhitosh 《Annals of Global Analysis and Geometry》2022,62(3):489-505
Annals of Global Analysis and Geometry - We prove Reilly-type upper bounds for divergence-type operators of the second order as well as for Steklov problems on submanifolds of Riemannian manifolds... 相似文献
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Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng. 相似文献
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We use minimal Legendrian submanifolds in spheres to construct examples of absolutely area-minimizing cones and we prove a result about Legendrian 2-tori in S5. 相似文献
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Yueshan XIONG 《Frontiers of Mathematics in China》2015,10(2):395
The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal q-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and (k, ?)-saddle submanifolds in Sasakian manifolds with positive transversal q-Ricci curvature are proved by using the weak (?-)asymptotic index. As a corollary, the Frankel type theorem is proved. 相似文献
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Bang-Yen Chen 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3561-3571
In this paper we initiate the study of Lagrangian submanifolds in para-Kähler manifolds. In particular, we prove two general optimal inequalities for Lagrangian submanifolds of the flat para-Kähler manifold . Moreover, we completely classify Lagrangian submanifolds which satisfy the equality case of one of the two inequalities. 相似文献
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