A note on surfaces with prescribed oriented Euclidean Gauss map
نویسندگان
چکیده
We present another proof of a theorem due to Hoffman and Osserman in Euclidean space concerning the determination of a conformal immersion by its Gauss map. Our approach depends on geometric quantities, that is, the hyperbolic Gauss map G and formulae obtained in hyperbolic space. We use the idea that the Euclidean Gauss map and the hyperbolic Gauss map with some compatibility relation determine a conformal immersion, proved in a previous paper.
منابع مشابه
L_1 operator and Gauss map of quadric surfaces
The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...
متن کاملTo Specify Surfaces of Revolution with Pointwise 1-type Gauss Map in 3-dimensional Minkowski Space
In this paper, by the studying of the Gauss map, Laplacian operator, curvatures of surfaces in R 1 and Bour’s theorem, we are going to identify surfaces of revolution with pointwise 1-type Gauss map property in 3−dimensional Minkowski space. Introduction The classification of submanifolds in Euclidean and Non-Euclidean spaces is one of the interesting topics in differential geometry and in this...
متن کاملThe Gauss Map for Surfaces: Part 1. the Affine Case
Let M be a connected oriented surface and let G'2 be the Grassmannian of oriented 2-planes in Euclidean (2 + c)-space. E2 + l. Smooth maps t: M -» (7f are studied to determine whether or not they are Gauss maps. Both local and global results are obtained. If í is a Gauss map of an immersion X: M -» E2 + 1, we study the extent to which / uniquely determines X under certain circumstances. Let X: ...
متن کاملThe Gauss Map of Minimal Surfaces in R
In this paper, we prove effective estimates for the number of exceptional values and the totally ramified value number for the Gauss map of pseudo-algebraic minimal surfaces in Euclidean four-space and give a kind of unicity theorem.
متن کاملA New Approach on Constant Angle Surfaces in E
In this paper we study constant angle surfaces in Euclidean 3–space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach to classify all surfaces for which the unit normal makes a constant angle with a fixed direction. Mathematics Subject Classification (2000): 53B25
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005