The Existence of Minimal Immersions of 2-Spheres
نویسنده
چکیده
منابع مشابه
Minimal Immersions of Spheres and Moduli
Minimal immersions of round spheres into round spheres, or spherical minimal immersions for short, or “spherical soap bubbles”, belong to a fast growing and fascinating area between algebra and geometry. This theory has rich interconnections with a variety of mathematical disciplines such as invariant theory, convex geometry, harmonic maps, and orthogonal multiplications. In this survey article...
متن کاملOn the Moduli of Isotropic and Helical Minimal Immersions between Spheres
DoCarmo-Wallach theory and its subsequent refinements assert the rich abundance of spherical minimal immersions, minimal immersions of round spheres into round spheres. A spherical minimal immersion can be written as a conformal minimal immersion f : Sm → SV with domain the Euclidean m-sphere Sm and range the unit sphere SV of a Euclidean vector space V . Takahashi’s theorem then implies that t...
متن کاملEigenmaps and the Space of Minimal Immersions between Spheres
In 1971 DoCarmo and Wallach gave a lower bound for the dimension of the space of minimal immersions between spheres and they believed that the lower estimate was sharp. We give here a different approach using conformal fields and eigenmaps; determine the exact dimension of this space and conclude that their conjecture is true.
متن کاملSpherical Minimal Immersions of Spherical Space Forms
Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ:M → S(r) ⊂ R is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace operator on M for the same eigenvalue. And conve...
متن کاملThe Spinor Representation of Surfaces in Space
The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan 33], which treats a spin structure on a Riemann surface M as a complex line bundle S whose square is the canonical line bundle K = T(M). Given a conformal immersion of M into R 3 , the unique spin strucure on S 2 pulls back via the Gauss map to a spin structur...
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 2010