JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE EXISTENCE OF WARPING FUNCTIONS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B)
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 36, Issue 3,  2014, pp.597-603
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2014.36.3.597
 Title & Authors
THE EXISTENCE OF WARPING FUNCTIONS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B)
Jung, Yoon-Tae; Lee, Ga-Young; Kim, A-Ryong; Lee, Soo-Young;
  PDF(new window)
 Abstract
In this paper, we prove the existence of warping functions on Riemannian warped product manifolds with fiber manifold of class (B) having some prescribed scalar curvatures.
 Keywords
warping function;Riemannian warped product manifold;scalar curvature;
 Language
English
 Cited by
1.
THE EXISTENCE OF SOME METRICS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B),;;;

Korean Journal of Mathematics, 2015. vol.23. 4, pp.733-740 crossref(new window)
1.
THE EXISTENCE OF SOME METRICS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B), Korean Journal of Mathematics, 2015, 23, 4, 733  crossref(new windwow)
 References
1.
J.K. Beem and P.E. Ehrlich, "Global Lorentzian Geometry", Pure and Applied Mathematics, 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.
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(2) June(2011).

4.
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.

5.
P.E. Ehrlich, Yoon-Tae Jung and Seon-Bu Kim, Constant scalar curvatures on warped product manifolds, Tsukuba J. Math. 20(1) (1996), 239-256.

6.
Y.T. Jung, Partial differential equations on semi-Riemannian manifolds, Journal of Mathematical Analysis and Applications 241 (2000), 238-253. crossref(new window)

7.
Y.T. Jung and In-Hae Kim, The nonexistence of warping functions on spacetimes, Honam Mathematical J. 30(4) Dec.(2008).

8.
Y.T. Jung, S.K. Kim, G.Y. Lee, S.Y. Lee and E.H. Choi, The existence of warping functions on Riemannian warped product manifolds, J.CHUNGCHEONG Math. Soc. 26(3) August(2013). crossref(new window)

9.
J.L. Kazdan and F.W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J. Diff. Geo. 10 (1975), 113-134.

10.
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. crossref(new window)

11.
J.L. Kazdan and F.W. Warner, Curvature functions for compact 2-manifolds, Ann. of Math. 99 (1974), 14-74. crossref(new window)

12.
M.C. Leung, Conformal scalar curvature equations on complete manifolds, Comm. in P.D.E. 20 (1995), 367-417 crossref(new window)

13.
M.C. Leung, Conformal deformation of warped products and scalar curvature functions on open manifolds, preprint.