EINSTEIN WARPED PRODUCT SPACES

  • KIM, DONG-SOO (Dept. of Mathematics, College of Natural Sciences, Chonnam National University)
  • Received : 2000.05.26
  • Published : 2000.07.30

Abstract

We study Einstein warped product spaces. As a result, we prove the following: if M is an Einstein warped product space with base a compact 2-dimensional surface, then M is simply a Riemannian product space.

Keywords

Acknowledgement

Supported by : Chonnam National University

References

  1. Global Lorentzian Geometry Beem, J.K.;Ehrlich, P.E.;Easley, K.L.
  2. Einstein Manifolds Besse, A.L.
  3. Trans. Amer. Math. Soc. v.145 Manifolds of negative curvature Bishop, R.L.;O'Neil, B.
  4. Bull. of Korean Math. Soc. v.35 no.4 A characterization of space forms Kim, D.S.;Kim, Y.H.
  5. Compact Einstein warped product spaces with nonpositive scalar curvature Kim, D.S.;Kim, Y.H.
  6. Conformal transformations between Einstein spaces;Conformal Geometry, Aspects of Math., E12 Kuhnel, W.
  7. Semi-Riemannian Geometry with applications to Relativity O'Neill, B.
  8. Proceedings of Differential Geometry Meeting Warped products and Einstein Manifolds (Joint work with A. Derdzinski and C. L. Terng) Palais, R.S.