scholarly journals IV. On the critical mean curvature of liquid surfaces of revolution

1887 ◽  
Vol 23 (140) ◽  
pp. 35-45 ◽  
Author(s):  
A.W. Rücker
Keyword(s):  
Mean Curvature ◽  
Surfaces Of Revolution ◽  
Liquid Surfaces

scholarly journals Constant curvature surfaces in a pseudo-isotropic space

2018 ◽  
Vol 49 (3) ◽  
pp. 221-233 ◽  
Author(s):  
Muhittin Evren Aydin
Keyword(s):  
Constant Curvature ◽  
Local Structure ◽  
Mean Curvature ◽  
Plane Curve ◽  
Surfaces Of Revolution ◽  
Curves And Surfaces ◽  
Isotropic Space ◽  
Constant Curvature Surfaces

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space $\mathbb{I}_{p}^{3}$ that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron for spacelike and timelike curves, respectively. The causal character of all admissible surfaces in $\mathbb{I}_{p}^{3}$ has to be timelike up to its absolute. We introduce the formulas of Gaussian and mean curvature for timelike surfaces in $\mathbb{I}_{p}^{3}$. As applications, we describe the surfaces of revolution which are the orbits of a plane curve under a hyperbolic rotation with constant Gaussian and mean curvature.

scholarly journals Singular surfaces of revolution with prescribed unbounded mean curvature

2019 ◽  
Vol 91 (3) ◽  
Author(s):  
MARTINS LUCIANA F. ◽  
KENTARO SAJI ◽  
SAMUEL P. DOS SANTOS ◽  
KEISUKE TERAMOTO
Keyword(s):  
Mean Curvature ◽  
Surfaces Of Revolution ◽  
Singular Surfaces

Examples of surfaces of constant mean curvature

2019 ◽  
pp. 148-154
Author(s):  
M. A. Cheshkova
Keyword(s):  
Gaussian Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Elliptic Integrals ◽  
Mathematical Software ◽  
Surfaces Of Revolution ◽  
Constant Gaussian Curvature ◽  
Constant Length ◽  
Positive Gaussian Curvature ◽  
Curvature Lines

A surface in E3 is called parallel to the surface M if it consists of the ends of constant length segments, laid on the normals to the surfaces M at points of this surface. The tangent planes at the corresponding points will be parallel. For surfaces in E3 the theorem of Bonnet holds: for any surface M that has constant positive Gaussian curvature, there exists a surface parallel to it with a constant mean curvature. Using Bonnet's theorem for a surfaces of revolution of constant positive Gaussian curvature, surfaces of constant mean curvature are constructed. It is proved that they are also surfaces of revolution. A family of plane curvature lines (meridians) is described by means of elliptic integrals. The surfaces of constant Gaussian curvature are also described by means of elliptic integrals. Using the mathematical software package, the surfaces under consideration are constructed.

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.

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