WILLMORE SURFACES AND F-WILLMORE SURFACES IN SPACE FORMS
نویسندگان
چکیده
منابع مشابه
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them holds...
متن کاملConstrained Willmore Surfaces
The aim of this article is to develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ H 2 dA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surf...
متن کامل5 Constrained Willmore Surfaces
We develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ HdA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surfaces in space forms.
متن کاملAnalysis Aspects of Willmore Surfaces
Abstract : We found a new formulation to the Euler-Lagrange equation of the Willmore functional for immersed surfaces in R. This new formulation of Willmore equation appears to be of divergence form, moreover, the nonlinearities are made of jacobians. Additionally to that, if ~ H denotes the mean curvature vector of the surface, this new form writes L ~ H = 0 where L is a well defined locally i...
متن کاملNew Examples of Willmore Surfaces in Sn
A surface x : M ! S n is called a Willmore surface if it is a critical surface of the Willmore functional R M (S ? 2H 2)dv, where H is the mean curvature and S is the square of the length of the second fundamental form. It is well-known that any minimal surface is a Willmore surface. The rst non-minimal example of a at Willmore surface in higher codimension was obtained by Ejiri. This example w...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2013
ISSN: 2224-6851,1027-5487
DOI: 10.11650/tjm.17.2013.2886