Abstract
We prove the nonexistence of an isometric immersion of the geometries Nil 3 and \(\widetilde{SL}_2\) into a four-dimensional space M 4c of constant curvature c. We establish that the geometry Sol 3 cannot be immersed into M 4c for c ≠ −1 and find the analytic immersion of this geometry into the hyperbolic space H 4 (−1).
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References
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 3, pp. 421–426, March, 2005.
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Masal'tsev, L.A. On Isometric Immersion of Three-Dimensional Geometries \(\widetilde{SL}_2\), Nil, and Sol into a Four-Dimensional Space of Constant Curvature. Ukr Math J 57, 509–516 (2005). https://doi.org/10.1007/s11253-005-0206-7
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DOI: https://doi.org/10.1007/s11253-005-0206-7