Compact Einstein warped product spaces with nonpositive scalar curvature
HTML articles powered by AMS MathViewer
- by Dong-Soo Kim and Young Ho Kim
- Proc. Amer. Math. Soc. 131 (2003), 2573-2576
- DOI: https://doi.org/10.1090/S0002-9939-03-06878-3
- Published electronically: February 26, 2003
- PDF | Request permission
Abstract:
We study Einstein warped product spaces. As a result, we prove the following: if $M$ is an Einstein warped product space with nonpositive scalar curvature and compact base, then $M$ is simply a Riemannian product space.References
- John K. Beem, Paul E. Ehrlich, and Kevin L. Easley, Global Lorentzian geometry, 2nd ed., Monographs and Textbooks in Pure and Applied Mathematics, vol. 202, Marcel Dekker, Inc., New York, 1996. MR 1384756
- Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. MR 867684, DOI 10.1007/978-3-540-74311-8
- R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1–49. MR 251664, DOI 10.1090/S0002-9947-1969-0251664-4
- Dennis M. DeTurck, Metrics with prescribed Ricci curvature, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 525–537. MR 645758
- S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry, Universitext, Springer-Verlag, Berlin, 1987. MR 909697, DOI 10.1007/978-3-642-97026-9
- B. O’Neill, Semi-Riemannian Geometry with applications to Relativity, Academic Press, New York (1983).
Bibliographic Information
- Dong-Soo Kim
- Affiliation: Department of Mathematics, College of Natural Sciences, Chonnam National University, Kwangju, 500-757, Korea
- Email: dosokim@chonnam.chonnam.ac.kr
- Young Ho Kim
- Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu, 702-701, Korea
- MR Author ID: 198019
- Email: yhkim@knu.ac.kr
- Received by editor(s): August 14, 2000
- Received by editor(s) in revised form: July 10, 2001
- Published electronically: February 26, 2003
- Additional Notes: This work was supported by the Brain Korea 21.
- Communicated by: Wolfgang Ziller
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2573-2576
- MSC (2000): Primary 53B20, 53C20
- DOI: https://doi.org/10.1090/S0002-9939-03-06878-3
- MathSciNet review: 1974657
Dedicated: Dedicated to Professor Bang-yen Chen on the occasion of his sixtieth birthday