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Ricci Tensors with Rotational Symmetry on R^n

Ronaldo Garcia·Romildo Pina
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Abstract

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 R^n. 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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Ronaldo Garcia, Romildo Pina. 2004-03-31. Ricci Tensors with Rotational Symmetry on R^n. https://arxiv.org/abs/math/0403544

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