Abstract
A definition of l -dimensional k-cylindrical metrics is introduced and it is proved that k-cylindrical metrics admit an immersion in the form of k-cylindrical surfaces into Lobachevsky space Ll+p, where codimension p of the immersion coincides with the codimension of the immersion of the base of the cylindrical metric into a Euclidean or Lobachevsky space.
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References
A. A. Borisenko, "Cylindrical multidimensional surfaces in Lobachevsky space," Ukrain. Geom. Sb., No. 33, 18–27 (1990).
A. A. Borisenko, "The extrinsic geometric properties of parabolic surfaces and topological properties of saddle surfaces in symmetric spaces of rank one," Mat. Sb.,116(158, No. 3(11), 440–457 (1981).
D. Ferus, "Totally geodesic foliations," Math. Ann.,188 No. 4, 313–317 (1970).
R. Maltz, "The nullity spaces of curvature-like tensors," J. Diff. Geom.,7 No. 3-4, 519–523 (1972).
Yu. Yu. Nut, Lobachevski Geometry From the Analytic Point of View [in Russian], Moscow (1961).
A. A. Borisenko and V. G. Ushakov, "The isometric immersion of strongly parabolic metrics in the class of strongly parabolic surfaces," Ukrain. Geom. Sb., No. 33, 27–36 (1990).
Additional information
Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 66–69, 1991.
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Lisitsa, V.T. Immersion ofn-dimensional cylindrical metrics in the form of cylindrical surfaces into Lobachevsky spaces. J Math Sci 69, 874–875 (1994). https://doi.org/10.1007/BF01250817
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DOI: https://doi.org/10.1007/BF01250817