Browse > Article
http://dx.doi.org/10.4134/BKMS.2009.46.1.061

A NOTE ON THE GENERALIZED MYERS THEOREM  

Yun, Jong-Gug (DEPARTMENT OF MATHEMATICS EDUCATION KOREA NATIONAL UNIVERSITY OF EDUCATION)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.1, 2009 , pp. 61-66 More about this Journal
Abstract
We provide a generalized Myers theorem under integral curvature bound and use this result to obtain a closure theorem in general relativity.
Keywords
Myers theorem; Ricci curvature;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 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.   과학기술학회마을
2 J. Beem, P. Ehrlich, and K. Easley, Global Lorentzian Geometry, 2nd edn., Marcel Dekker, New York, 1996.
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.   DOI
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 G. J. Galloway, A generalization of Myers' theorem and an application to relativistic cosmology, J. Differential Geom. 14 (1979), no. 1, 105–116   DOI
6 S.-H. Paeng, Singularity theorem with weak timelike convergence condition, Preprint.
7 C. Sprouse, Integral curvature bounds and bounded diameter, Comm. Anal. Geom. 8 (2000), no. 3, 531–543.   DOI
8 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.   DOI
9 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.
10 P. E. Ehrlich and M. S´anchez, Some semi-Riemannian volume comparison theorems, Tohoku Math. J. (2) 52 (2000), no. 3, 331–348.   DOI
11 T. Frankel and G. J. Galloway, Energy density and spatial curvature in general relativity, J. Math. Phys. 22 (1981), no. 4, 813–817.   DOI