ON WARPED PRODUCT MANIFOLDS - CONFORMAL FLATNESS AND CONSTANT SCALAR CURVATURE PROBLEM

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Published: Sep 1, 1998
DOI: https://doi.org/10.5556/j.tkjm.29.1998.4272
Keywords:
Warped porduct conformal flat scalar curvature

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KWANG-WU YANG
Yuan-Ze Institute of Technology, Energy Technology Center, 135 Yuan-Tung Road., Ne-Li, Taoyuan Shian, Taiwan 32026, R.O.C.

Abstract




In this paper, we study some geometric properties on doubly or singly warped­ product manifolds. In general, on a fixed topological product manifold, the problem for finding warped-product metrics satisfying certain curvature conditions are finally reduced to find positive solutions of linear or non-linear differential equations. Here, we are mainly interested in the following problems on essentially warped-product manifolds: one is the sufficient and necessary conditions for conformal flatness, and the other is to find warped-product metrics so that their scalar curvatures are contants.




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How to Cite
YANG, K.-W. (1998). ON WARPED PRODUCT MANIFOLDS - CONFORMAL FLATNESS AND CONSTANT SCALAR CURVATURE PROBLEM. Tamkang Journal of Mathematics, 29(3), 203–221. https://doi.org/10.5556/j.tkjm.29.1998.4272
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Vol. 29 No. 3 (1998)
Section
Papers
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