scholarly journals Hasimoto surfaces in Galilean space $$G_{3}$$

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
M. Elzawy
Keyword(s):  
Mean Curvature ◽  
Gauss Curvature ◽  
Galilean Space

AbstractIn this article Hasimoto surfaces in Galilean space $$G_{3}$$ G 3 will be considered, Gauss curvature (K) and Mean curvature (H) of Hasimoto surfaces $$\chi =\chi (s,t)$$ χ = χ ( s , t ) will be investigated, some characterization of s-curves and t-curves of Hasimoto surfaces in Galilean space $$G_{3}$$ G 3 will be introduced. Example of Hasimoto surfaces will be illustrated.

scholarly journals Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

2014 ◽  
Vol 12 (9) ◽  
Author(s):  
Rafael López ◽  
Esma Demir
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Curvature ◽  
First Case ◽  
Helicoidal Surfaces ◽  
Constant Gauss Curvature

AbstractWe classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

Translating Solitons of the Mean Curvature Flow Asymptotic to Hyperplanes in ℝn+1

2018 ◽  
Vol 2020 (24) ◽  
pp. 10114-10153 ◽  
Author(s):  
Eddygledson S Gama ◽  
Francisco Martín
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Normal Component ◽  
Vertical Cylinder ◽  
Curvature Flow ◽  
Grim Reaper ◽  
The Family ◽  
The Mean ◽  
Translating Solitons

Abstract A translating soliton is a hypersurface $M$ in ${\mathbb{R}}^{n+1}$ such that the family $M_t= M- t \,\mathbf e_{n+1}$ is a mean curvature flow, that is, such that normal component of the velocity at each point is equal to the mean curvature at that point $\mathbf{H}=\mathbf e_{n+1}^{\perp }.$ In this paper we obtain a characterization of hyperplanes that are parallel to the velocity and the family of tilted grim reaper cylinders as the only translating solitons in $\mathbb{R}^{n+1}$ that are $C^1$-asymptotic to two half-hyperplanes outside a non-vertical cylinder. This result was proven for translators in $\mathbb{R}^3$ by the 2nd author, Perez-Garcia, Savas-Halilaj, and Smoczyk under the additional hypotheses that the genus of the surface was locally bounded and the cylinder was perpendicular to the translating velocity.

scholarly journals Characterization of facet breaking for nonsmooth mean curvature flow in the convex case

2001 ◽  
pp. 415-446 ◽  
Author(s):  
Giovanni Bellettini ◽  
Matteo Novaga ◽  
Maurizio Paolini
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Convex Case

scholarly journals Unitarization of Loop Group Representations of Fundamental Groups

2007 ◽  
Vol 187 ◽  
pp. 1-33 ◽  
Author(s):  
Josef Dorfmeister ◽  
Hongyou Wu
Keyword(s):  
Fundamental Group ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Loop Group ◽  
Fundamental Groups ◽  
Matrix Functions ◽  
Group Representations ◽  
Constant Mean Curvature Surfaces ◽  
Finite Set

AbstractIn this paper, we give a characterization of the simultaneous unitarizability of any finite set of SL(2, ℂ)-valued functions on and determine all possible ways of the unitarization. Such matrix functions can be regarded as images of the generators for the fundamental group of a surface in an -family, and the results of this paper have applications in the construction of constant mean curvature surfaces in space.

scholarly journals A new characterization of submanifolds with parallel mean curvature vector in $S^{n+p}$

2004 ◽  
Vol 27 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Abd\^enago Alves de Barros ◽  
Aldir Chaves Brasil Jr. ◽  
Luis Amancio Machado de Soursa Jr.
Keyword(s):  
Mean Curvature ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Parallel Mean Curvature
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