Yamabe problem [SEP] named after
Yamabe problem
The Yamabe problem in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature, and takes its name from the mathematician Hidehiko Yamabe. claimed to have a solution, but discovered a critical error in his proof. The combined work of Neil Trudinger, Thierry Aubin, and Richard Schoen later provided a complete solution to the problem in 1984.
The Yamabe problem is the following: Given a smooth, compact manifold of dimension with a Riemannian metric , does there exist a metric conformal to for which the
Weyl–Schouten theorem
The Weyl–Schouten theorem in mathematics (named after Hermann Weyl and Jan Arnoldus Schouten) says that a Riemannian manifold of dimension "n" with "n" ≥ 3 is conformally flat if and only if the Schouten tensor is a Codazzi tensor for "n" = 3, or the Weyl tensor vanishes for "n"  3.
See also.
- Yamabe problem