# Riemannian Topology Meeting

8-9 November 2018
University of Fribourg, Switzerland
Europe/Berlin timezone

## Scalar curvature and the multiconformal class of a direct product Riemannian manifold

8 Nov 2018, 15:05
50m
University of Fribourg, Switzerland

### Speaker

For a closed, connected direct product Riemannian manifold $(M,g) = (M_1 \times \ldots \times M_l, g_1 + \ldots + g_l)$ we define its multiconformal class $[\![ g ]\!]$ as the totality $\lbrace f_1^2 g_1 + \ldots + f_l^2 g_l \rbrace$ of all Riemannian metrics obtained from multiplying the metric $g_i$ of each factor by a function $f_i^2:M \rightarrow \mathbb{R}_+$. In this talk we discuss how constant scalar curvature metrics in a multiconformal class are related with constant scalar curvature metrics on the factors.