A note on the scalar curvature problem in the presence of symmetries
The scalar curvature problem considered in this paper is the following: which function \(K\) on the standard sphere is the scalar curvature of a conformally equivalent metric? In this paper it is assumed that the function \(K\) is invariant under a subgroup \(G\) of the orthogonal group \({\mathbb O}(n+1)\) with fixed point set Fix\(=S^n \cap (\{(0,0,\ldots,0)\}\times {\mathbb R}^{n+1-k})\). Under certain regularity assumptions for the positive and \(G\)-invariant function \(K\) a sufficient condition in terms of invariants of an expansion of \(K\) at the critical fixed points is shown.
scientific article; zbMATH DE number 1846949