Compact Lorentzian manifolds without closed nonspacelike geodesics

Author:
Gregory J. Galloway

Journal:
Proc. Amer. Math. Soc. **98** (1986), 119-123

MSC:
Primary 53C50; Secondary 53C22

MathSciNet review:
848888

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every compact two-dimensional Lorentzian manifold contains a closed timelike or null geodesic. We then construct a two-dimensional example without any closed timelike geodesies and a three-dimensional example without any closed timelike or null geodesics.

**[1]**John K. Beem and Paul E. Ehrlich,*Global Lorentzian geometry*, Monographs and Textbooks in Pure and Applied Math., vol. 67, Marcel Dekker, Inc., New York, 1981. MR**619853****[2]**Gregory J. Galloway,*Closed timelike geodesics*, Trans. Amer. Math. Soc.**285**(1984), no. 1, 379–388. MR**748844**, 10.1090/S0002-9947-1984-0748844-6**[3]**Gregory J. Galloway,*Splitting theorems for spatially closed space-times*, Comm. Math. Phys.**96**(1984), no. 4, 423–429. MR**775039****[4]**Robert P. Geroch,*Topology in general relativity*, J. Mathematical Phys.**8**(1967), 782–786. MR**0213139****[5]**S. W. Hawking and G. F. R. Ellis,*The large scale structure of space-time*, Cambridge University Press, London-New York, 1973. Cambridge Monographs on Mathematical Physics, No. 1. MR**0424186****[6]**Barrett O’Neill,*Semi-Riemannian geometry*, Pure and Applied Mathematics, vol. 103, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With applications to relativity. MR**719023****[7]**Roger Penrose,*Techniques of differential topology in relativity*, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1972. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 7. MR**0469146****[8]**Frank J. Tipler,*Existence of closed timelike geodesics in Lorentz spaces*, Proc. Amer. Math. Soc.**76**(1979), no. 1, 145–147. MR**534406**, 10.1090/S0002-9939-1979-0534406-6

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
53C50,
53C22

Retrieve articles in all journals with MSC: 53C50, 53C22

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0848888-7

Article copyright:
© Copyright 1986
American Mathematical Society