Ricci Tensors with Rotational Symmetry on Rⁿ
Garcia, Ronaldo · Pina, Romildo
Original · EN
In this paper is considered the differential equation Ric(g)=T, where Ric(g) is the Ricci tensor of the metric g and T is a rotational symmetric tensor on Rⁿ. A new, geometric, proof of the existence of smooth solutions of this equation, based on qualitative theory of implicitdifferential equations, is presented here. This result was obtained previously by DeTurck and Cao in 1994.
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