The Yamabe problem for higher order curvatures
Let M be a compact Riemannian manifold of dimension n > 2. The k-curvature, for k = 1,2, . . . , n, is defined as the k-th elementary symmetric polynomial of the eigenvalues of the Schouten tenser. The k-Yamabe problem is to prove the existence of a conformal metric whose k-curvature is a constant. When k = 1, it reduces to the well-known Yamabe problem. Under the assumption that the metric is admissible, the existence of solutions is known for the case k = 2, n = 4, for locally conformally...[Show more]
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|Source:||Journal of Differential Geometry|
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