Complete Constant Mean Curvature Surfaces in Euclidean Three-Space

1990 ◽  
Vol 131 (2) ◽  
pp. 239 ◽  
Author(s):  
Nicolaos Kapouleas
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Surfaces ◽  
Euclidean Three Space ◽  
Three Space

scholarly journals Delaunay surfaces expressed in terms of a Cartan moving frame

2020 ◽  
Vol 26 (1) ◽  
pp. 153-160
Author(s):  
Paul Bracken
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Elliptic Functions ◽  
Moving Frame ◽  
Jacobi Elliptic Functions ◽  
Surfaces Of Revolution ◽  
Constant Mean Curvature Surfaces ◽  
The Mean ◽  
Euclidean Three Space ◽  
Three Space

AbstractDelaunay surfaces are investigated by using a moving frame approach. These surfaces correspond to surfaces of revolution in the Euclidean three-space. A set of basic one-forms is defined. Moving frame equations can be formulated and studied. Related differential equations which depend on variables relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case in which the mean curvature is constant, these functions can be expressed in terms of Jacobi elliptic functions.

scholarly journals Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair

2004 ◽  
Vol 2004 (15) ◽  
pp. 755-762 ◽  
Author(s):  
Paul Bracken
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Lax Pair ◽  
Moving Frame ◽  
Lax Representation ◽  
Euclidean Three Space ◽  
Three Space ◽  
Codazzi Equations

The moving frame and associated Gauss-Codazzi equations for surfaces in three-space are introduced. A quaternionic representation is used to identify the Gauss-Weingarten equation with a particular Lax representation. Several examples are given, such as the case of constant mean curvature.

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