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Volume ratios of a hypersurface relative to the FLRW space-time

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초록

We calculate volume ratio of a hypersurface orthogonal to a timelike geodesic relative to that of a hypersurface in the FLRW space-time.

Abstract

We calculate volume ratio of a hypersurface orthogonal to a timelike geodesic relative to that of a hypersurface in the FLRW space-time.

참고문헌 (10)

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  3. J. R. Kim, "Erratum to The upperbound of the volume expansion rate in a Lorentzian manifold", Gen. Relativity Gravitation, 42(12), pp.2981~2982 (2010)
  4. J. R. Kim, "Relative Lorentzian volume comparison with integral Ricci and scalar curvature bound", J. Geom. Phys, 61(6), pp.1061~1069 (2011)
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  6. B. O’Neil, "Semi-Riemannian Geometry with applications to Relativity" (1983), Pure Appl. Math., Academic Press
  7. S. -H. Paeng, "Volume expansion rate of the Lorentzian manifold based on integral Ricci curvature over a timelike geodesic", J. Geom. Phys, 57(6), pp.1499~1503 (2007)
  8. P. Petersen, "Integral curvature bounds, distance estimates and applica-tions", J. Differential Geom, 50(2), pp.269~298 (1998)
  9. P. Petersen, "Relative volume comparison with integral curvature bounds", Geom. Funct. Anal, 7(6), pp.1031~1045 (1997)
  10. J. -G. Yun, "Volume comparison for Lorentzian warped products with integral curvature bounds", J. Geom. Phys, 57(3), pp.903~912 (2007)

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