Quasi-minimal Lorentz surfaces with pointwise 1-type Gauss map in pseudo-Euclidean 4-space

To 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...

Minimal Surfaces in Euclidean Space

A note on surfaces with prescribed oriented Euclidean Gauss map

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 determin...

The Gauss Map for Surfaces : Part 2 . the Euclidean Case

We study smooth maps t: M -> Ci of a Riemann surface M into the Grassmannian Gi of oriented 2-planes in E2 ' ' and determine necessary and sufficient conditons on t in order that it be the Gauss map of a conformai immersion X: M -» E2 + '. We sometimes view / as an oriented riemannian vector bundle; it is a subbundle of Ej/'. the trivial bundle over M with fibre E2 + l. The necessary and suffic...

Value Distribution Theoretical Properties of the Gauss Map of Pseudo-algebraic Minimal Surfaces

In this thesis, we study value distribution theoretical properties of the Gauss map of pseudo-algebraic minimal surfaces in ndimensional Euclidean space. After reviewing basic facts, we give estimates for the number of exceptional values and the totally ramified value numbers and the corresponding unicity theorems for them.