Pacific Journal of Mathematics

Klein-Gordon solvability and the geometry of geodesics.

John K. Beem and Phillip E. Parker

Article information

Source
Pacific J. Math., Volume 107, Number 1 (1983), 1-14.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102720734

Mathematical Reviews number (MathSciNet)
MR701803

Zentralblatt MATH identifier
0518.53062

Subjects
Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics

Citation

Beem, John K.; Parker, Phillip E. Klein-Gordon solvability and the geometry of geodesics. Pacific J. Math. 107 (1983), no. 1, 1--14. https://projecteuclid.org/euclid.pjm/1102720734


Export citation

References

  • [12] Since the bicharacteristics of the Laplacian are points, every Rieman- nian manifold is -pseudoconvex. Geodesic pseudoconvexity is a natural variant, and is studied in 5. Principal causality is equivalent tothe condition that no inextendible causal geodesic lies in a compact set. Indeed, any integral curve of a (fiber homogeneous) vector field which stays in (or over) a compact set is complete. However, thecoordinates
  • [K] C K'. By Lemma 3.3, via the observation above, [K\ is closed.D
  • [4] Lorentzian theory. In this section several known results for spacetimes are generalized to Lorentzian manifolds and new sufficient conditions are given for the existence of a causal geodesic segment joining two causally related points. According to the Hopf-Rinow Theorem [8, p.
  • [1] J. Beem and P. Ehrlich, Global Lorentzian Geometry, New York: Marcel Dekker, 1981.
  • [2] J. Beem, P. Ehrlich and T. Powell, Warped product manifolds in relativity, in Einstein volume, Athens: North Holland, 1982.
  • [3] J. J. Duistermaat and L. Hrmander, Fourier integral operators II, Acta. Math., 128 (1972), 183-269.
  • [4] F. Flaherty, Lorentzian manifolds of nonpositie curvature, in Proc. Symp. Pure Math.
  • [5] F. G. Friedlander, The Wave Equation on a Curved Space-time, Cambridge, 1975.
  • [6] S. Hawking and G. Ellis, The Large Scale Structure of Space-time, Cambridge, 1973.
  • [7] S. Hawking and R. Sachs, Causally continuous spacetimes, Commun. Math. Phys., 35 (1975), 287-296.
  • [8] N. Hicks, Notes on Differential Geometry, Princeton: Van Nostrand, 1965.
  • [9] S. Lang, Differential Manifolds, Reading: Addison-Wesley, 1972.
  • [10] B. O'Neill, Semi-riemannian Geometry, New York: Academic Press, 1983.
  • [11] P. E. Parker, Distributional geometry, J. Math. Phys., 20 (1979), 1423-1426.
  • [12] P. E. Parker, Mathematical Relativity, Syracuse University lecture notes, 1979.
  • [13] M. Taylor, Pseudodifferential Operators, Princeton, 1981.