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Compact Einstein warped product spaces with nonpositive scalar curvature
Author(s):
Dong-Soo
Kim;
Young
Ho
Kim
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2573-2576.
MSC (2000):
Primary 53B20, 53C20
Posted:
February 26, 2003
MathSciNet review:
1974657
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Abstract:
We study Einstein warped product spaces. As a result, we prove the following: if  is an Einstein warped product space with nonpositive scalar curvature and compact base, then  is simply a Riemannian product space.
References:
-
- 1.
- J. K. Beem, P. E. Ehrlich and K. L. Easley, Global Lorentzian Geometry (2nd ed.), Marcel Dekker, Inc., New York (1996). MR 97f:53100
- 2.
- A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin-Heidelberg (1987). MR 88f:53087
- 3.
- R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. MR 40:4891
- 4.
- D. DeTurck, Metrics with prescribed Ricci curvature, Seminar on Differential Geometry (S. T. Yau, ed.), Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, NJ (1982), 525-537. MR 83e:53014
- 5.
- S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Springer-Verlag, Berlin (1987). MR 88k:53001
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- B. O'Neill, Semi-Riemannian Geometry with applications to Relativity, Academic Press, New York (1983).
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Additional 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
Email:
yhkim@knu.ac.kr
DOI:
10.1090/S0002-9939-03-06878-3
PII:
S 0002-9939(03)06878-3
Keywords:
Einstein space,
warped product,
Ricci tensor,
Hessian tensor,
Ricci identity
Received by editor(s):
August 14, 2000
Received by editor(s) in revised form:
July 10, 2001
Posted:
February 26, 2003
Additional Notes:
This work was supported by the Brain Korea 21.
Dedicated:
Dedicated to Professor Bang-yen Chen on the occasion of his sixtieth birthday
Communicated by:
Wolfgang Ziller
Copyright of article:
Copyright
2003,
American Mathematical Society
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