Naslov
On Wingarten surfaces in some projective-metric spaces
(On Weingarten surfaces in some projective-metric spaces)

Autori
Divjak, Blaženka ; Milin Šipuš, Željka

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Abstracts - 4th Croatian Mathematical Congres / Scitovski, Rudolf - Osijek : Odjel za matematiku Sveučilišta Josipa Jurja Strossmayera u Osijeku, 2008, 23-23

Skup
4th Croatian Mathematical Congres

Mjesto i datum
Osijek, Hrvatska, 17.06.2008. - 20.06.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Weingarten surfaces; first and second fundamental form

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA