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THE COMPLETENESS OF SOME METRICS ON LORENTZIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B)

  • Jung, Yoon-Tae (Department of Mathematics, Chosun University) ;
  • Lee, Jeong-Mi (Department of Mathematics Education, Graduate School of Education, Chosun University) ;
  • Lee, Ga-Young (Department of Mathematics, Graduate School, Chosun University)
  • Received : 2015.02.24
  • Accepted : 2015.03.01
  • Published : 2015.03.25

Abstract

In this paper, we prove the existence of warping functions on Lorentzian warped product manifolds and the completeness of the resulting metrics with some prescribed scalar curvatures.

Keywords

References

  1. J. K. Beem and P. E. Ehrlich, Global Lorentzian Geometry, Pure and Applied Mathematics, Vol.67, Dekker, New York, 1981.
  2. J. K. Beem, P. E. Ehrlich and Th. G. Powell, Warped product manifolds in relativity, Selected Studies (Th.M. Rassias, G.M. Rassias, eds.), North-Holland, 1982, 41-56.
  3. F. Dobarro and E. Lami Dozo, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. I.H.E.S. 58 (1983), 295-408.
  4. P.E. Ehrlich, Y.-T. Jung and S.-B. Kim, Constant scalar curvatures on warped product manifolds, Tsukuba J. Math. 20 no.1 (1996), 239-256. https://doi.org/10.21099/tkbjm/1496162996
  5. Y.-T. Jung, Partial differential equations on semi-Riemannian manifolds, Journal of Mathematical Analysis and Applications 241(2000), 238-253. https://doi.org/10.1006/jmaa.1999.6640
  6. J. L. Kazdan and F. W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J.Diff.Geo. 10(1975), 113-134. https://doi.org/10.4310/jdg/1214432678
  7. J. L. Kazdan and F. W. Warner, Existence and conformal deformation of metrics with prescribed Guassian and scalar curvature, Ann. of Math. 101(1975), 317-331. https://doi.org/10.2307/1970993
  8. J. L. Kazdan and F. W. Warner, Curvature functions for compact 2 - manifolds, Ann. of Math. 99(1974), 14-74. https://doi.org/10.2307/1971012
  9. M. C. Leung, Conformal scalar curvature equations on complete manifolds, Comm. in P.D.E. 20 (1995), 367-417 https://doi.org/10.1080/03605309508821100
  10. M. C. Leung, Conformal deformation of warped products and scalar curvature functions on open manifolds, preprint.
  11. T. G. Powell, Lorentzian manifolds with non-smooth metrics and warped products, Ph.D thesis, Univ. of Missouri-Columbia, 1982.