Nonhomothetic complete periodic metrics with constant scalar curvature
Abstract
We show that there are infinitely many pairwise nonhomothetic, complete, periodic metrics with constant scalar curvature that are conformal to the round metric on S n ∖ S k S^n\setminus S^k , where k > n − 2 2 k > \frac {n-2}{2} . These metrics are obtained by pulling back Yamabe metrics defined on products of S n − k − 1 S^{n-k-1} and compact hyperbolic ( k + 1 ) (k+1) -manifolds. The core of our argument relies on classical rigidity theorems due to Obata [J. Differential Geometry 6 (1971/72), pp. 247–258] and Ferrand [Math. Ann. 304 (1996), pp. 277–291], which characterize the round sphere by its conformal group.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Fixed Point Theorems Analysis
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 10
- Pages
- 4505–4518
- Publication date
- 17 June 2026
- Language
- EN