Pacific Journal of Mathematics

Klein-Gordon solvability and the geometry of geodesics.

John K. Beem and Phillip E. Parker

Article information

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

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Beem, John K.; Parker, Phillip E. Klein-Gordon solvability and the geometry of geodesics. Pacific J. Math. 107 (1983), no. 1, 1--14.

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  • [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.
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