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Extrema in Space-Time

Published online by Cambridge University Press:  20 November 2018

Louis V. Quintas  and
Fred Supnick
Louis V. Quintas
Affiliation:
St. John's University, New York and The City University of New York
Fred Supnick
Affiliation:
St. John's University, New York and The City University of New York
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Consider an astronomer and his observation field, i. e., the set of observable (light or radio) signal-emitting loci of the universe. Let the observation field be ordered by attaching a date to each observable locus indicating the time in the history of the universe that the signal was emitted from its source. Whereas both the astronomer and his observation field age with time, the observations of the astronomer may trace a sequence of loci whose time labels proceed forward or backward in time (cf. Appendix).

Consider now a finite set S of events in Ln,n-dimensional space-time (Riemannian n-space having the fundamental form

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 678 - 691
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Supnick, F., Extreme Hamiltonian lines, Ann. Math. (2), 66 (1957), 179–201.Google Scholar
2. Supnick, F. and Quintas, L. V., Extreme Hamiltonian circuits. Resolution of the convex-odd case, Proc. Amer. Math. Soc., 15 (1964), 454–456.Google Scholar
3. Quintas, L. V. and Supnick, F., Extreme Hamiltonian circuits. Resolution of the convex-even case, Proc. Amer. Math. Soc, 16 (1965), 1058–1061.Google Scholar
4. Quintas, L. V. and Supnick, F., On some properties of shortest Hamiltonian circuits, Amer. Math. Monthly, 72 (1965), 977–980.Google Scholar