Naslov
Minimal invariant and minimal totally real submanifolds in Sol_0^4

Autori
Erjavec, Zlatko ; Inoguchi, Jun-ichi

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

Izvornik
Abstracts - 5th Croatian Conference on Geometry and Graphics / Došlić, Tomislav ; Jurkin, Ema - Zagreb, 2022, 16-16

Skup
5th Croatian Conference on Geometry and Graphics

Mjesto i datum
Dubrovnik, Hrvatska, 04.09.2022. - 08.09.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
4-dimensional geometry ; minimal submanifold ; solvable Lie group ; LCK structure

Sažetak
The space Sol_0^4 is one of the 19 model spaces of 4-dimensional Thurston geometries which belongs to non-Kaehler model spaces. It is known that the Hermitian structures of all non-Kaehler model spaces are locally conformal Kaehler. We consider minimal invariant and minimal totally real submanifolds in the 4-dimensional homogeneous solvable Lie group Sol_0^4 equipped with standard globally conformal Kaehler structure. We prove that the only minimal invariant surfaces of Sol_0^4 are totally geodesic hyperbolic planes. This is quite different from a situation in Kaehler model spaces where holomorphic curves are automatically minimal. We show that minimal totally real surfaces in Sol_0^4 tangent or normal to the Lee vector field are cylindrical surfaces.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA