충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제26권3호
  • /
  • Pages.525-532
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  • 2013
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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THE EXISTENCE OF WARPING FUNCTIONS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS

  • 투고 : 2013.03.27
  • 심사 : 2013.07.16
  • 발행 : 2013.08.15
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초록

In this paper, when N is a compact Riemannian manifold of class (A), we consider the existence of some warping functions on Riemannian warped product manifolds $M=[a,{\infty}){\times}_fN$ with prescribed scalar curvatures.

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과제정보

연구 과제 주관 기관 : Chosun University

참고문헌

  1. E-.H. Choi, Y-.H. Yang and S-.Y. Lee, The nonexistence of warping functions on Riemannian warped product manifolds, J. Chungcheong Math. Soc. 24 (2011), no. 2, 171-185.
  2. F. Dobarro and E. Lami Dozo, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. I. H. E. S. 58 (1893), 295-408.
  3. P. E. Ehrlich, Yoon-Tae Jung and Seon-Bu Kim, Constant scalar curvatures on warped product manifolds, Tsukuba J. Math. 20 (1996), no. 1, 239-256. https://doi.org/10.21099/tkbjm/1496162996
  4. M. Gromov and H. B. Lawson, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Math. I. H. E. S. 58 (1983), 295-408.
  5. Y. T. Jung and I. H. Kim, The Nonexistence of Warping Functions On Space-Times, Honam Mathematical J. 30 (2008), no. 4, 693-701. https://doi.org/10.5831/HMJ.2008.30.4.693
  6. J. L. Kazdan and F. W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J. DiR.Geo. 10 (1975), 113-134.
  7. J. L. Kazdan and F. W. Warner, Existence and conformal deformation of metrics with prescribed Gaussian 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.

피인용 문헌

  1. THE EXISTENCE OF WARPING FUNCTIONS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B) vol.36, pp.3, 2014, https://doi.org/10.5831/HMJ.2014.36.3.597