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http://dx.doi.org/10.11568/kjm.2015.23.4.733

THE EXISTENCE OF SOME METRICS ON RIEMANNIAN WARPED PRODUCT MANIFOLDS WITH FIBER MANIFOLD OF CLASS (B)  

JUNGY, YOON-TAE (Department of Mathematics Chosun University)
CHAE, SONG-HWA (Department of Mathematics Chosun University)
LEE, SOO-YOUNG (Department of Mathematics Chosun University)
Publication Information
Korean Journal of Mathematics / v.23, no.4, 2015 , pp. 733-740 More about this Journal
Abstract
In this paper, we prove the existence of warping functions on Riemannian warped product manifolds with some prescribed scalar curvatures according to the fiber manifolds of class (B).
Keywords
warping function; Riemannian warped product manifold; scalar curvature;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 P. Aviles and R. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, DiR. Geom. 27 (1998), 225-239.
2 J. Bland and M. Kalka, Negative scalar curvature metrics on non-compact manifolds, Trans. Amer. Math. Soc. 316 (1989), 433-446.   DOI
3 R.L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49.   DOI
4 E-H Choi, Y-H Yang and S-Y Lee, The nonexistence of warping functuins on Riemannian warped product manifolds, J. Chungcheong Math. Soc. 24 (2011) (2), 171-185.
5 F. Dobarro and E. Lami Dozo, Positive scalar curvature and the Dirac operater on complete Riemannian manifolds, Publ. Math.I.H.E.S. 58 (1983), 295-408.
6 M. Gromov and H.B. Lawson, positive scalar curvature and the Dirac operater on complete Riemannian manifolds, Math. I.H.E.S. 58 (1983), 295-408.
7 Y-T Jung, G-Y Lee, A-R Kim and S-Y Lee, The existence of warping functuins on Riemannian warped product manifolds with fiber manifold of class (B), Honam Math. J. 36 (2014) (3), 597-603.   DOI
8 H. Kitabara, H. Kawakami and J.S. Pak, On a construction of completely simply connected Riemmannian manifolds with negative curvature, Nagoya Math. J. 113 (1980), 7-13.
9 J.L. Kazdan and F.W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J. Diff. Geo 10 (1975), 113-134.   DOI
10 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.   DOI
11 J.L. Kazdan and F.W. Warner, Curvature functions for compact 2-manifolds, Ann. of Math. 99(1974), 14-74.   DOI
12 M.C. Leung, Conformal scalar curvature equations on complete manifolds, Commum. Partial Diff. Equation 20 (1995), 367-417.   DOI
13 M.C. Leung, Conformal deformation of warped products and scalar curvature functions on open manifolds, Bulletin des Science Math-ematiques. 122 (1998), 369-398.   DOI
14 H.B. Lawson and M. Michelsohn, Spin geometry, Princeton University Press, Princeton, (1989).
15 X. Ma and R.C. Mcown, The Laplacian on complete manifolds with warped cylindrical ends, Commum. Partial Diff. Equation 16 (1991),1583-1614.   DOI
16 S. Zucker, $L_2$ cohomology of warped products and arithmetric groups, Invent. Math. 70 (1982), 169-218.   DOI