Search results for: Thomas Hasanis

Items from 1 to 7 out of 7 results

article

Classification and Construction of Minimal Translation Surfaces in Euclidean Space

Thomas Hasanis, Rafael López

Results in Mathematics > 2020 > 75 > 1 > 1-22

A translation surface of Euclidean space $${\mathbb {R}}^3$$ R3 is the sum of two regular curves $$\alpha $$ α and $$\beta $$ β , called the generating curves. In this paper we classify the minimal translation surfaces of $${\mathbb {R}}^3$$ R3 and we give a method of construction of explicit examples. Besides the plane and the minimal surfaces of Scherk type, it is proved that up to reparameterizations...

article

Translation surfaces with non-zero constant mean curvature in Euclidean space

Thomas Hasanis

Journal of Geometry > 2019 > 110 > 2 > 1-8

We prove that the only surface in 3-dimensional Euclidean space $${\mathbb {R}}^3$$ R3 with constant and non-zero mean curvature H, constructed by the sum of a planar curve and a space curve, is the circular cylinder of radius $$\frac{1}{2|H|}$$ 12|H| .

article

Hypersurfaces and Codazzi tensors

Thomas Hasanis, Theodoros Vlachos

Monatshefte für Mathematik > 2008 > 154 > 1 > 51-58

. In this paper we deal with the following problem. Let (M ⁿ,〈,〉) be an n-dimensional Riemannian manifold and $f:(M^{n},\langle \,,\rangle)\rightarrow {\Bbb R}^{n+1}$ an isometric immersion. Find all Riemannian metrics on M ⁿ that can be realized isometrically as immersed hypersurfaces in the Euclidean space ${\Bbb R}^{n+1}$ . More precisely, given another Riemannian metric $\widetilde{{\langle \,,\rangle }}$ ...

article

Complete Minimal Hypersurfaces in a Sphere

Thomas Hasanis, Andreas Savas-Halilaj, Theodoros Vlachos

Monatshefte für Mathematik > 2005 > 145 > 4 > 301-305

. In this paper we investigate complete minimal hypersurfaces $f : M^{n}\rightarrow {\Bbb S}^{n+1}$ with at most two principal curvatures. We prove that if the squared norm S of the second fundamental form satisfies S ≥ n, then S = n and f(M ⁿ) is a minimal Clifford torus.

article

On convex hypersurfaces in $E^{n+1}$

Thomas Hasanis

Colloquium Mathematicum > 1984 > 48 > 1 > 49-55

article

Characterizations of the sphere by the curvature of the second fundamental form

Thomas Hasanis

Colloquium Mathematicum > 1982 > 46 > 1 > 41-44

article

A new characterization of the sphere in $R^3$

Thomas Hasanis

Annales Polonici Mathematici > 1980 > 38 > 1 > 47-49

Let M be a closed connected surface in $R^3$ with positive Gaussian curvature K and let $K_II$ be the curvature of its second fundamental form. It is shown that M is a sphere if $K_II = c√HK^r$, for some constants c and r, where H is the mean curvature of M.

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Search results for: Thomas Hasanis

Classification and Construction of Minimal Translation Surfaces in Euclidean Space

Translation surfaces with non-zero constant mean curvature in Euclidean space

Hypersurfaces and Codazzi tensors

Complete Minimal Hypersurfaces in a Sphere

On convex hypersurfaces in $E^{n+1}$

Characterizations of the sphere by the curvature of the second fundamental form

A new characterization of the sphere in $R^3$

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INFONA - science communication portal

Search results for: Thomas Hasanis

Classification and Construction of Minimal Translation Surfaces in Euclidean Space

Translation surfaces with non-zero constant mean curvature in Euclidean space

Hypersurfaces and Codazzi tensors

Complete Minimal Hypersurfaces in a Sphere

On convex hypersurfaces in $E^{n+1}$

Characterizations of the sphere by the curvature of the second fundamental form

A new characterization of the sphere in $R^3$

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