대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제46권1호
  • /
  • Pages.61-66
  • /
  • 2009
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON THE GENERALIZED MYERS THEOREM

  • Yun, Jong-Gug (DEPARTMENT OF MATHEMATICS EDUCATION KOREA NATIONAL UNIVERSITY OF EDUCATION)
  • 발행 : 2009.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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

키워드

참고문헌

  1. J. Beem, P. Ehrlich, and K. Easley, Global Lorentzian Geometry, 2nd edn., Marcel Dekker, New York, 1996.
  2. C. Chicone and P. Ehrlich, Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds, Manuscripta Math. 31 (1980), no. 1-3, 297-316. https://doi.org/10.1007/BF01303279
  3. P. E. Ehrlich, Y.-T. Jung, and S.-B. Kim, Volume comparison theorems for Lorentzian manifolds, Geom. Dedicata 73 (1998), no. 1, 39–56. https://doi.org/10.1023/A:1005096913126
  4. P. E. Ehrlich, Y.-T. Jung, J.-S. Kim, and S.-B. Kim, Jacobians and volume compar-ison for Lorentzian warped products, Recent advances in Riemannian and Lorentzian geometries (Baltimore, MD, 2003), 39–52, Contemp. Math., 337, Amer. Math. Soc., Providence, RI, 2003.
  5. P. E. Ehrlich and S.-B. Kim, From the Riccati inequality to the Raychaudhuri equa-tion, Differential geometry and mathematical physics (Vancouver, BC, 1993), 65–78,Contemp. Math., 170, Amer. Math. Soc., Providence, RI, 1994.
  6. P. E. Ehrlich and M. S´anchez, Some semi-Riemannian volume comparison theorems, Tohoku Math. J. (2) 52 (2000), no. 3, 331–348. https://doi.org/10.2748/tmj/1178207817
  7. T. Frankel and G. J. Galloway, Energy density and spatial curvature in general relativity, J. Math. Phys. 22 (1981), no. 4, 813–817. https://doi.org/10.1063/1.524961
  8. G. J. Galloway, A generalization of Myers' theorem and an application to relativistic cosmology, J. Differential Geom. 14 (1979), no. 1, 105–116 https://doi.org/10.4310/jdg/1214434856
  9. S.-B. Kim and D.-S. Kim, A focal Myers-Galloway theorem on space-times, J. Korean Math. Soc. 31 (1994), no. 1, 97–110.
  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 (2000), no. 3, 531–543. https://doi.org/10.4310/CAG.2000.v8.n3.a4

피인용 문헌

  1. Compactness in Weighted Manifolds and Applications vol.68, pp.1-2, 2015, https://doi.org/10.1007/s00025-014-0427-x
  2. A NOTE ON THE GENERALIZED MYERS THEOREM FOR FINSLER MANIFOLDS vol.50, pp.3, 2013, https://doi.org/10.4134/BKMS.2013.50.3.833