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A note on the generalized Myers theorem

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초록

We provide a generalized Myers theorem under integral curvature bound and use this result to obtain a closure theorem in general relativity.

Abstract

We provide a generalized Myers theorem under integral curvature bound and use this result to obtain a closure theorem in general relativity.

참고문헌 (11)

  1. J. Beem, "Global Lorentzian Geometry" (1996), Marcel Dekker
  2. C. Chicone, "Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds", Manuscripta Math, 31(1), pp.297~316 (1980)
  3. P. E. Ehrlich, "Volume comparison theorems for Lorentzian manifolds", Geom. Dedicata, 73(1), pp.39~56 (1998)
  4. P. E. Ehrlich, "Jacobians and volume compar-ison for Lorentzian warped products, Recent advances in Riemannian and Lorentzian geometries", Contemp. Math., Amer. Math. Soc.,Providence, RI, 337, pp.39~52 (2003)
  5. P. E. Ehrlich, "From the Riccati inequality to the Raychaudhuri equa-tion, Differential geometry and mathematical physics", Contemp. Math., Amer. Math. Soc., Providence, 170, pp.65~78 (1994)
  6. P. E. Ehrlich, "Some semi-Riemannian volume comparison theorems", Tohoku Math. J., 52(3), pp.331~348 (2000)
  7. T. Frankel, "Energy density and spatial curvature in general relativity", J. Math. Phys., 22(4), pp.813~817 (1981)
  8. G. J. Galloway, "A generalization of Myers' theorem and an application to relativistic cosmology", J. Differential Geom., 14(1), pp.105~116 (1979)
  9. S.-B. Kim, "A focal Myers-Galloway theorem on space-times", J. Korean Math. Soc., 31(1), pp.97~110 (1994)
  10. S.-H. Paeng, "Singularity theorem with weak timelike convergence condition", Preprint
  11. C. Sprouse, "Integral curvature bounds and bounded diameter", Comm. Anal. Geom., 8(3), pp.531~543 (2000)

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