Polynomial Translation Weingarten Surfaces in 3-dimensional Euclidean Space

نویسندگان

  • MARIAN IOAN MUNTEANU
  • IOAN MUNTEANU
  • IRINA NISTOR
چکیده

In this paper we will classify those translation surfaces in E involving polynomials which are Weingarten surfaces. Mathematics Subject Classification (2000): 53A05, 53A10.

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

Translation surfaces according to a new frame

In this paper we studied the translation surfaces according to a new frame called q-frame in three dimensional Euclidean space. The curvatures of the translation surface are obtained in terms of q-frame curvatures. Finally some special cases are investigated for these surfaces.

متن کامل

Linear Weingarten Helicoidal Surfaces in Isotropic Space

Introduced in 1861 [1], a Weingarten surface in the Euclidean three-dimensional space E3 is a surface M, whose mean curvature H and Gaussian curvature K satisfy a non-trivial relation Φ(H, K) = 0. Such a surface was introduced by Weingarten. The class of Weingarten surfaces is remarkably large, and it consists of intriguing surfaces in the Euclidean space: the constant mean curvature surfaces, ...

متن کامل

Linear Weingarten surfaces in Euclidean and hyperbolic space

In this paper we review some author’s results about Weingarten surfaces in Euclidean space R 3 and hyperbolic space H 3 . We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property. First, we consider Weingarten surfaces in R 3 that are foliated by circles, proving that the surface is rotational, a Riemann example or a generalized cone. Next...

متن کامل

On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal su...

متن کامل

Rotational linear Weingarten surfaces of hyperbolic type

A linear Weingarten surface in Euclidean space R 3 is a surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH + bK = c, where a, b, c ∈ R. Such a surface is said to be hyperbolic when a + 4bc < 0. In this paper we classify all rotational linear Weingarten surfaces of hyperbolic type. As a consequence, we obtain a family of complete hyperbolic linear Weingarte...

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 2008