Journal ArticleDOI
Metric and Periodic Lines in de Sitter’s World
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In this paper, the authors determine all metric and periodic lines in de Sitter's world over a real pre-Hilbert space, and show that all lines in this space are periodic.Abstract:
We determine all metric and periodic lines in de Sitter’s world over a real pre-Hilbert space.read more
Citations
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Journal ArticleDOI
Studies in Geometry. By L. M. Blumenthal and K. Menger. Pp. xiv, 512. £7. 1970. (Freeman.)
Journal ArticleDOI
The cogyrolines of Möbius gyrovector spaces are metric but not periodic
TL;DR: In this article, it was shown that every metric line of a Mobius gyrovector space is exactly a cogyroline of itself, and also proved the nonexistence of periodic lines in this space.
Journal ArticleDOI
Is There Any Metric Line Which Can Be Represented By A Single Fixed Point
TL;DR: In this article, a special metric line example which can be written by using a single fixed point is presented, and the nonexistence of periodic lines in Levenberg plane is proved.
References
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Book
The Large Scale Structure of Space-Time
TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.
Journal ArticleDOI
Studies in Geometry. By L. M. Blumenthal and K. Menger. Pp. xiv, 512. £7. 1970. (Freeman.)
Journal ArticleDOI
On the Ramsey numbers R(3, 8) and R(3, 9)
TL;DR: Using methods developed by Graver and Yackel, and various computer algorithms, it is shown that 28 ≤ R (3, 8) ≤ 29, and R ( 3, 9) = 36, where R ( k , l ) is the classical Ramsey number for 2-coloring the edges of a complete graph.
Journal ArticleDOI
Metric and Periodic Lines in Real Inner Product Space Geometries
TL;DR: The lines of euclidean and hyperbolic geometries are characterized as metric lines in the sense of Blumenthal-Menger, and the lines of spherical and elliptic geometry as periodic ones.