Spherical rigidities of submanifolds in Euclidean spaces
نویسندگان
چکیده
منابع مشابه
Classification of Spherical Lagrangian Submanifolds in Complex Euclidean Spaces
An isometric immersion f : Mn → M̃n from a Riemannian nmanifold Mn into a Kähler n-manifold M̃n is called Lagrangian if the complex structure J of the ambient manifold M̃n interchanges each tangent space of Mn with the corresponding normal space. In this paper, we completely classify spherical Lagrangian submanifolds in complex Euclidean spaces. In this paper, we also provide two corresponding cla...
متن کاملPolyharmonic submanifolds in Euclidean spaces
B.Y. Chen introduced biharmonic submanifolds in Euclidean spaces and raised the conjecture ”Any biharmonic submanifold is minimal”. In this article, we show some affirmative partial answers of generalized Chen’s conjecture. Especially, we show that the triharmonic hypersurfaces with constant mean curvature are minimal. M.S.C. 2010: 58E20, 53C43.
متن کاملSpherical Submanifolds of a Euclidean Space
A1 and A2 being arbitrary constants. A natural generalization of this question to higher dimensions could be: ‘given an isometric immersion ψ : Mn → Rn+2 of a compact n-dimensional Riemannian manifold (Mn, g), obtain conditions for ψ(Mn) ⊂ Sn+1(c), where Sn+1(c) is the sphere of constant curvature c’. We write ψT , ψ⊥ as tangential and normal components of the position vector ψ in Rn+p and show...
متن کاملComplex Extensors and Lagrangian Submanifolds in Complex Euclidean Spaces
Lagrangian //-umbilical submanifolds are the "simplest" Lagrangian submanifolds next to totally geodesic ones in complex-space-forms. The class of Lagrangian //-umbilical submanifolds in complex Euclidean spaces includes Whitney's spheres and Lagrangian pseudo-spheres. For each submanifold M of Euclidean «-space and each unit speed curve F in the complex plane, we introduce the notion of the co...
متن کاملOn Indefinite Special Lagrangian Submanifolds in Indefinite Complex Euclidean Spaces
In this paper, we show that the calibrated method can also be used to detect indefinite minimal Lagrangian submanifolds in C k . We introduce the notion of indefinite special Lagrangian submanifolds in C k and generalize the well-known work of Harvey-Lawson to the indefinite case.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2004
ISSN: 0025-5645
DOI: 10.2969/jmsj/1191418640