On Some Weingarten Surfaces in the Special Linear Group SL(2,R)

On Some Weingarten Surfaces in the Special Linear Group SL(2,R)

We classify Weingarten conoids in the real special linear group SL(2,R). In particular, there is no linear Weingarten nontrivial conoids in SL(2,R). We also prove that the only conoids in SL(2,R) with constant Gaussian curvature are the flat ones. Finally, we show that any surface that is invariant...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematics (Basel) 2023-11, Vol.11 (22), p.4636
1. Verfasser: Munteanu, Marian Ioan
Format: Artikel
Sprache:eng
Schlagworte:
<named-content content-type="inline-formula"><mml:math display="block" id="mm11111111"><mml:mi mathvariant="script">N</mml:mi></mml:math></named-content>-surfaces
Algebra
conoids
Decomposition
Geometry
Linear algebraic groups
Mathematical research
rotational surfaces
special linear group
Subgroups
Translations
Weingarten surfaces
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We classify Weingarten conoids in the real special linear group SL(2,R). In particular, there is no linear Weingarten nontrivial conoids in SL(2,R). We also prove that the only conoids in SL(2,R) with constant Gaussian curvature are the flat ones. Finally, we show that any surface that is invariant under left translations of the subgroup N is a Weingarten surface.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11224636