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A particular case of the problem of precribed scalar curcature in \(S^n\). (Un caso particular del problema de prescribir la curvatura escalar en \(S^n\).) (Spanish. English summary) Zbl 1153.53304

Summary: In this paper we exhibit a family of metrics which are conformal to the Euclidean metric on the unit sphere in \(\mathbb R^{n+1}\) and such that \(K=n(n-1)\) is its scalar curvature. To obtain this family we use stereographic projection, conformal transforms of dilatation and pullback of the metric.

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53A05 Surfaces in Euclidean and related spaces
53A30 Conformal differential geometry (MSC2010)
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