SPECIAL SURFACES IN R3

Milos Kanka

Abstract


The principal objects of this paper are regular parametrical surfaces in . The method we want to use is based on Weingarten mapping. We suppose that the mapping , where   and , is regular. Symbols  and  are used in this paper instead of ,  etc. These vectors form the basis of tangent space  (see Fig.1). On  we can construct moving frame ( ). Vectors  and  are tangent vector fields of ,  is a normal vector field  and


is a unit normal vector field. In this paper we are going to study Gauss and Mean curvature of some classical surfaces with methods based on Weingarten mapping


Keywords


Weingarten Map, first and second fundamental forms, structural equations, Gaussian and Mean curvature.

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References


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