COMPARISON OF EINSTEIN MANIFOLDS WITH THORPE MANIFOLDS

  • Kim, Ho-Bub (Department of Mathematics, Yonsei University) ;
  • Kim, Jae-Man (Department of Mathematics, Yonsei University)
  • Published : 2000.02.01

Abstract

On Riemannian manifolds of dimension 4 the Einstein condition is equivalent to the Thorpe condition. In this paper, we construct a few metrics which we Einstein but not Thorpe, and vice versa in dimensions larger than 4.

Keywords

Einstein condition;Thorpe condition

References

  1. Annals of Mathematics v.80 Sectional curvatures and characteristic classes J.A. Thorpe
  2. Einstein-Thorpe Manifolds J.M.Kim
  3. Journal of Mathematics and Mechanics v.18 Some remarks on the Gauss-Bonnet integral
  4. Einstein manifolds A.L. Besse