2018
Том 70
№ 1

# On Isometric Immersion of Three-Dimensional Geometries $SL_2$, $Nil$ and $Sol$ into a Four-Dimensional Space of Constant Curvature

Masal'tsev L. A.

Abstract

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 $H^4(-1)$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 3, pp 509-516.

Citation Example: Masal'tsev L. A. On Isometric Immersion of Three-Dimensional Geometries $SL_2$, $Nil$ and $Sol$ into a Four-Dimensional Space of Constant Curvature // Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 421–426.

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