Scalar curvature along Ebin geodesics

07.11.2024, 16:15 Uhr  –  Raum 0.14
Forschungsseminar Differentialgeometrie

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.