I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 1, PAGES 299-303
N. E. Maryukova
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A three-dimensional quasi-Riemann space of constant curvature can be Galilean, quasi-elliptic or quasi-hyperbolic depending on the sign of the curvature. The results obtained by the author for the Galilean case are generalized to the case of quasi-elliptic and quasi-hyperbolic spaces. It is shown that the curvature radius of special lines as well as the angle between asymptotic lines on the surface of constant negative (positive) curvature in quasi-elliptic (quasi-hyperbolic) space satisfy one-dimensional Klein--Gordon equation
and, in addition, for the surfaces of quasi-elliptic space, which
have Gaussian curvature with absolute value equal to that of
the space curvature,
The existence of surfaces corresponding to any given solution of Klein--Gordon equation is shown, the families of surfaces for some special class of such solutions are constructed.
All articles are published in Russian.
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Last modified: April 11, 2000