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Indefinite Finsler Spaces and Timelike Spaces

Published online by Cambridge University Press:  20 November 2018

John K. Beem
John K. Beem*
Affiliation:
University of Missouri, Columbia, Missouri
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In this paper we investigate indefinite Finsler spaces in which the metric tensor has signature n — 2. These spaces are a generalization of Lorentz manifolds. Locally a partial ordering may be defined such that the reverse triangle inequality holds for this partial ordering. Consequently, the spaces we study may be made into what Busemann [3] terms locally timelike spaces. Furthermore, sufficient conditions are obtained for an indefinite Finsler space to be a doubly timelike surface (see [2; 4]). In particular, all two-dimensional pseudo-Riemannian spaces are shown to be doubly timelike surfaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 1035 - 1039
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Beem, J. K., Indefinite Minkowski spaces, Pacific J. Math. 33 (1970), 29–42.Google Scholar
2. Beem, J. K. and Woo, P. Y., Doubly timelike surfaces, Mem. Amer. Math. Soc. No. 92, 1969.Google Scholar
3. Busemann, H., Timelike spaces, Dissertationes Math. Rozprawy Mat. 53 (1967), 52 pp.Google Scholar
4. Busemann, H. and Beem, J. K., Axioms for indefinite metrics, Rend. Circ. Mat. Palermo (2) 15 (1966), 223–246.Google Scholar
5. Whitehead, J. H. C., Convex regions in the geometry of paths—Addendum, Quart. J. Math. Oxford Ser. 4 (1933), 226–227.Google Scholar