On Isometric Immersion of Three-Dimensional Geometries $SL_2$, $Nil$ and $Sol$ into a Four-Dimensional Space of Constant Curvature
We prove the nonexistence of isometric immersion of geometries $\text{Nil}^3$, $\widetilde{SL}_2$ into the four-dimensional space $M_c^4$ of the constant curvature $c$. We establish that the geometry $\text{Sol}^3$ cannot be immersed into $M_c^4$ if $c \neq -1$ and find the analytic immersion of thi...
Gespeichert in:
| Datum: | 2005 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2005
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3609 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We prove the nonexistence of isometric immersion of geometries $\text{Nil}^3$, $\widetilde{SL}_2$ into the four-dimensional space $M_c^4$ of the constant curvature $c$. We establish that the geometry $\text{Sol}^3$ cannot be immersed into $M_c^4$ if $c \neq -1$ and find the analytic immersion of this geometry into the hyperbolic space $H^4(-1)$.
|
|---|