
CHRISTOPH BÖHM, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada 
Inhomogeneous Einstein metrics on spheres 
The standard metric on the ndimensional sphere S^{n} is Einstein, i.e. its Ricci tensor is a multiple of itself. The first nontrivial example of an Einstein metric on S^{n} was given by Jensen for n=4m+3 in 1973. Five years later Bourguignon and Karcher described a further Einstein metric on S^{15}. Up to now these metrics were the only known examples of Einstein metrics on spheres. All of them are homogeneous and Ziller proved that there exists no further homogeneous Einstein metric on S^{n}. We describe infinitely many inhomogeneous Einstein metrics with positive scalar curvature on S^{5}, S^{6}, S^{7}, S^{8}, S^{9}. The resulting sequence of Einstein metrics converges to an explicit known limit metric which is smooth outside two submanifolds. Hence we get new examples of manifolds where the PalaisSmale condition for the total scalar curvature functional is not fulfiled.