Ricci Tensors with Rotational Symmetry on R^n

Details Ricci Tensors with Rotational Symmetry on R^n Ricci Tensors with Rotational Symmetry on R^n

2004-03-31

arxiv.org/abs/math/0403544v1

Mathematics

Differential Geometry

12 pages, 01 figure. To appear in Resenhas do IME-USP

Scientific paper

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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