Geodesic
Indefinite Finsler Spaces and Timelike Spaces
Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 1035-1039

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Beem, John K. Indefinite Finsler Spaces and Timelike Spaces. Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 1035-1039. doi: 10.4153/CJM-1970-119-7
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[1] 1. Beem, J. K., Indefinite Minkowski spaces, Pacific J. Math. 33 (1970), 29–42. Google Scholar

[2] 2. Beem, J. K. and Woo, P. Y., Doubly timelike surfaces, Mem. Amer. Math. Soc. No. 92, 1969. Google Scholar

[3] 3. Busemann, H., Timelike spaces, Dissertationes Math. Rozprawy Mat. 53 (1967), 52 pp. Google Scholar

[4] 4. Busemann, H. and Beem, J. K., Axioms for indefinite metrics, Rend. Circ. Mat. Palermo (2) 15 (1966), 223–246. Google Scholar

[5] 5. Whitehead, J. H. C., Convex regions in the geometry of paths—Addendum, Quart. J. Math. Oxford Ser. 4 (1933), 226–227. Google Scholar

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