Results 21 to 30 of about 1,097 (74)

An approach for minimal surface family passing a curve

, 2014
We investigate minimal surfaces passing a given curve in $R^{3}$. Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for minimal surface.
Kahyaoğlu, Sedat, Kasap, Emin
core   +1 more source

Minimal Darboux transformations

, 2016
We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-
Hertrich-Jeromin, U., Honda, A.
core   +1 more source

Type I+ Helicoidal Surfaces with Prescribed Weighted Mean or Gaussian Curvature in Minkowski Space with Density

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
In this paper, we construct a helicoidal surface of type I+ with prescribed weighted mean curvature and Gaussian curvature in the Minkowski 3−space ℝ13${\Bbb R}_1^3$with a positive density function. We get a result for minimal case.
Yıldız Önder Gökmen, Hızal Selman, Akyiğit Mahmut   +2 more
doaj   +1 more source

On the Gauss map of embedded minimal tubes

, 1999
A surface is called a tube if its level-sets with respect to some coordinate function (the axis of the surface) are compact. Any tube of zero mean curvature has an invariant, the so-called flow vector. We study how the geometry of the Gaussian image of a
Reshetnikova, Irina M., Tkachev, Vladimir G.   +1 more
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Sphere-foliated minimal and constant mean curvature hypersurfaces in product spaces [PDF]

, 2010
In this paper, we prove that minimal hypersurfaces when $n\geq 3$ and nonzero constant mean curvature hypersurfaces when $n\geq2$ foliated by spheres in parallel horizontal hyperplanes in ${\mathbb{H}}^n \times \mathbb{R}$ must be rotationally symmetric ...
Seo, Keomkyo
core   +1 more source

Compact surfaces with no Bonnet mate

, 2017
This note gives sufficient conditions (isothermic or totally nonisothermic) for an immersion of a compact surface to have no Bonnet mate.Comment: 7 pages ...
Jensen, Gary R., Musso, Emilio, Nicolodi, Lorenzo   +2 more
core   +1 more source

On constant higher order mean curvature hypersurfaces in Hn×R ${\mathbb{H}}^{n}{\times}\mathbb{R}$

Advanced Nonlinear Studies
We classify hypersurfaces with rotational symmetry and positive constant r-th mean curvature in Hn×R ${\mathbb{H}}^{n}{\times}\mathbb{R}$ . Specific constant higher order mean curvature hypersurfaces invariant under hyperbolic translation are also ...
Nelli Barbara, Pipoli Giuseppe, Russo Giovanni   +2 more
doaj   +1 more source

Survey on real forms of the complex A2(2)-Toda equation and surface theory

Complex Manifolds, 2019
The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups [9] states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop ...
Dorfmeister Josef F., Freyn Walter, Kobayashi Shimpei, Wang Erxiao   +3 more
doaj   +1 more source

Disc stackings and their Morse index

Advanced Nonlinear Studies
We construct free boundary minimal disc stackings, with any number of strata, in the three-dimensional Euclidean unit ball, and prove uniform, linear lower and upper bounds on the Morse index of all such surfaces. Among other things, our work implies for
Carlotto Alessandro, Schulz Mario B., Wiygul David   +2 more
doaj   +1 more source

An eigenvalue estimate for self-shrinkers in a Ricci shrinker

Advanced Nonlinear Studies
In this paper, we study the drifted Laplacian Δf on a hypersurface M in a Ricci shrinker (M̄,g,f) $\left(\bar{M},g,f\right)$ . We prove that the spectrum of Δf is discrete for immersed hypersurfaces with bounded weighted mean curvature in a Ricci ...
Conrado Franciele, Zhou Detang
doaj   +1 more source