Extrema of curvature functionals on the space of metrics on 3-manifolds. II (Q5927663)

This article, a continuation of a previous paper [the author, Calc. Var. Partial Differ. Equ. 5, 199-269 (1997; Zbl 0889.58027)] is concerned with rigidity questions for 3-dimensional Riemmannian manifolds. The author studies the (non)-existence of critical metrics for the functional given by the square of the Ricci curvature. The first main result: A complete critical metric with nonnegative scalar curvature must be flat. Additional results of similar nature are obtained for metrics with scalar curvature constraints.