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On Weingarten surfaces in some projective-metric spaces (CROSBI ID 540172)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Divjak, Blaženka ; Milin Šipuš, Željka On Weingarten surfaces in some projective-metric spaces // Abstracts - 4th Croatian Mathematical Congres / Scitovski, Rudolf (ur.). Osijek: Odjel za matematiku Sveučilišta Josipa Jurja Strossmayera u Osijeku, 2008. str. 23-23

Podaci o odgovornosti

Divjak, Blaženka ; Milin Šipuš, Željka

engleski

On Weingarten surfaces in some projective-metric spaces

In this presentation we consider a wide class of immersed surfaces in some special projective--metric spaces -- Weingarten surfaes. The ambient space for studying these surfaces are the Euclidean, Minkowski and the Galilean space. Weingarten surfaces are surfaces having non-trivial functional connection between their Gaussian $K$ and mean curvature $H$. They include surfaces of constant curvature, as well minimal surfaces and surfaces of constant mean curvature. A sphere is a linear Weingarten surface in all mentioned spaces. In Euclidean space the only ruled non-developable Weingarten surface is a piece of a helicoidal surface, in particular a ruled non-developable minimal surface is a right helicoid, whereas in Minkowski space there are several surfaces with that property: a piece of a helicoidal surface with non-null rulings and a ruled surface with null rullings satisfying $H^2=K$. In particular, a ruled non-developable minimal surface in Minkowski space is either a piece of a Cayley's ruled surface or a piece of a three Lorentzian helicoids. In Galilean space ruled non-developable Weingarten surfaces are helicoidal ruled surfaces, hyperboloids of one-sheet and hyperbolic paraboloids. Furthermore, in the mentioned spaces it is possible to consider Weingarten surfaces with Gaussian curvature which was generated as the inner curvature of the second fundamental form of the surfaces. Finally, some tranformations between pseudospherical surfaces (surfaces with constant negative curvature) connecting surfaces of these kind will also be considered in the mentioned spaces (B\"{; ; a}; ; cklund transformations). They can be extended to transformations between Weingarten surfaces as well.

Weingarten surfaces; first and second fundamental form

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Podaci o prilogu

23-23.

2008.

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objavljeno

Podaci o matičnoj publikaciji

Abstracts - 4th Croatian Mathematical Congres

Scitovski, Rudolf

Osijek: Odjel za matematiku Sveučilišta Josipa Jurja Strossmayera u Osijeku

Podaci o skupu

4th Croatian Mathematical Congres

predavanje

17.06.2008-20.06.2008

Osijek, Hrvatska

Povezanost rada

Matematika