Christoph Böhm (Münster)
Let \(M^n\) be a smooth, compact manifold and let \(N\) denote the set of Riemannian metrics on \(M^n\) with a fixed smooth volume density \(\mu\) of volume 1. For any \(g_0 \in N\) , we show that if \(n \geq 5\) then there exists an open and dense subset \(Y \subset T_{g_0} N\) so that, for each \(h \in Y\) the Ebin geodesic \(\gamma_h(t)\) with \(\gamma_h(0)=g_0\) and \(\gamma_h'(0)=h\) satisfies \(\lim_{ t \to +\infty} R(\gamma_h(t))=-\infty\), uniformly on \(M^n\), where \(R\) denotes scalar curvature.
