Willmore Legendrian surfaces in pseudoconformal 5-sphere
نویسنده
چکیده
where B0 is the trace free part of the second fundamental form of X. It was introduced by Willmore in a slightly different but equivalent form for surfaces in E. The functional is invariant under conformal transformation, and it is natural to extend it for submanifolds in conformal N -sphere S = E ∪ {∞}. Willmore conjecture asks if Clifford torus in S is the unique minimizer of W(X) among all immersed tori. Li and Yau introduced the notion of conformal area of a compact Riemann surface, and showed that Willmore conjecture is true if the induced complex(conformal) structure
منابع مشابه
Willmore Surfaces of R 4 and the Whitney Sphere ?
We make a contribution to the study of Willmore surfaces in four-dimensional Euclidean space R4 by making use of the identification of R4 with two-dimensional complex Euclidean space C2. We prove that the Whitney sphere is the only Willmore Lagrangian surface of genus zero in R4 and establish some existence and uniqueness results about Willmore Lagrangian tori in R4 ≡ C2. Mathematics Subject Cl...
متن کاملAdjoint Transform of Willmore Surfaces in n-sphere
After the surface theory of Möbius geometry, this study concerns a pair of conformally immersed surfaces in n-sphere. Two new invariants θ and ρ associated with them are introduced as well as the notion of touch and co-touch. This approach is helpful in research about transforms of certain surface classes. As an application, we define adjoint transform for any given Willmore surface in n-sphere...
متن کاملWillmore Two-spheres in the Four-sphere
Genus zero Willmore surfaces immersed in the three-sphere S3 correspond via the stereographic projection to minimal surfaces in Euclidean three-space with finite total curvature and embedded planar ends. The critical values of the Willmore functional are 4πk, where k ∈ N∗, with k 6= 2, 3, 5, 7. When the ambient space is the four-sphere S4, the regular homotopy class of immersions of the two-sph...
متن کاملA PINCHING THEOREM FOR CONFORMAL CLASSES OF WILLMORE SURFACES IN THE UNIT n-SPHERE BY YU-CHUNG CHANG AND YI-JUNG HSU
Let x : M →S be a compact immersed Willmore surface in the n-dimensional unit sphere. In this paper, we consider the case of n ≥ 4. We prove that if infg∈G maxg◦x(M)(Φg − 1 8 H g −
متن کاملWillmore Surfaces of Constant Möbius Curvature
We study Willmore surfaces of constant Möbius curvature K in S. It is proved that such a surface in S must be part of a minimal surface in R or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in S of constant K could only be part of a complex curve in C ∼= R or the Veronese 2-sphere in S. It is conjectured that they are the only examples possi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008