Constant angle surfaces in Minkowski space

نویسندگان

  • Rafael López
  • Marian Ioan Munteanu
چکیده

A constant angle surface in Minkowski space is a spacelike surface whose unit normal vector field makes a constant hyperbolic angle with a fixed timelike vector. In this work we study and classify these surfaces. In particular, we show that they are flat. Next we prove that a tangent developable surface (resp. cylinder, cone) is a constant angle surface if and only if the generating curve is a helix (resp. a straight-line, a circle).

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

$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $mathbb{E}_1^4$

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

متن کامل

Translation Surfaces of the Third Fundamental Form in Lorentz-Minkowski Space

In this paper we study translation surfaces with the non-degenerate third fundamental form in Lorentz- Minkowski space $mathbb{L}^{3}$. As a result, we classify translation surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form $III$ on the surface.

متن کامل

Helicoidal Surfaces and Their Gauss Map in Minkowski 3-space

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

متن کامل

Constant Mean Curvature Surfaces in Euclidean and Minkowski 3-spaces

Spacelike constant mean curvature surfaces in Minkowski 3-space L have an infinite dimensional generalized Weierstrass representation. This is analogous to that given by Dorfmeister, Pedit and Wu for constant mean curvature surfaces in Euclidean space, replacing the group SU(2) with SU(1, 1). The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop grou...

متن کامل

The harmonic evolute of a surface in Minkowski 3-space

In this paper we describe harmonic evolutes of surfaces in Minkowski 3-space. In particular, we study properties of harmonic evolutes of constant mean curvature surfaces and their relation to parallel surfaces. Furthermore, we study harmonic evolutes of surfaces of revolution. AMS subject classifications: 53A35, 53B30

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 2009