Explicit Parametrization of Delaunay Surfaces in Space Forms via Loop Group Methods

نویسندگان

  • NAHID SULTANA
  • H. Wu
چکیده

We compute explicit conformal parametrizations of Delaunay surfaces in each of the three space forms Euclidean 3-space , spherical 3-space 3 and hyperbolic 3-space 3 by using the generalized Weierstrass type representation for constant mean curvature (CMC) surfaces established by J. Dorfmeister, F. Pedit and H. Wu.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Constant Mean Curvature Surfaces with Delaunay Ends in 3-dimensional Space Forms

This paper presents a unified treatment of constant mean curvature (cmc) surfaces in the simply-connected 3-dimensional space forms R, S and H in terms of meromorphic loop Lie algebra valued 1-forms. We discuss global issues such as period problems and asymptotic behaviour involved in the construction of cmc surfaces with nontrivial topology. We prove existence of new examples of complete non-s...

متن کامل

Cmc Surfaces In

This paper presents a unified treatment of constant mean curvature (CMC) surfaces in the simply-connected 3-dimensional space forms R 3 , S 3 and H 3 in terms of meromorphic loop Lie algebra valued 1-forms. We discuss global issues such as period problems and asymptotic behaviour involved in the construction of CMC surfaces with non-trivial topology. We prove existence of new examples of comple...

متن کامل

Unitarization of Monodromy Representations and Constant Mean Curvature Trinoids in 3-dimensional Space Forms

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms R, S and H. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.

متن کامل

Surfaces Generated by Translation Surfaces of Type 1 in I^1_3

In this paper, we classify surface at a constant distance from the edge of regression on translation surfaces of Type 1 in the three dimensional simply isotropic space I^1_3 satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these ...

متن کامل

Exploring the Space of Compact Symmetric Cmc Surfaces

We map out the moduli space of Lawson symmetric constant mean curvature surfaces in the 3-sphere of genus g > 1 by flowing numerically from Delaunay tori with even lobe count via the generalized Whitham flow. 1. Overview. In this note we map out a portion of the moduli space of embedded constant mean curvature (CMC) surfaces in the 3-sphere experimentally by a numerical implementation of the ge...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005