The scalar curvature equation on \(S^3\). (English) Zbl 1201.53042
Let \(S^3\) be the standard sphere with round metric \(g_0\). The problem studied here is to find the functions K on \(S^3\) which occur as scalar curvature of metrics \(g\) conformally equivalent to \(g_0\). The present paper gives some existence results for solutions of the prescribed scalar curvature equation on \(S^3\), when the curvature function is a positive Morse function and satisfies an index-count condition.
Reviewer: Cornelia-Livia Bejan (Iaşi)
MSC:
| 53C20 | Global Riemannian geometry, including pinching |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
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