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Free keywords:
Mathematics, Differential Geometry, math.DG,General Relativity and Quantum Cosmology, gr-qc,
Abstract:
A family of non-radial solutions of the Yamabe equation, with reference the
hyperbolic space, is constructed using power series. As a result, we obtain a
family of asymptotically hyperbolic metrics, with spherical conformal infinity,
with scalar curvature greater than -n(n - 1), but which are a priori not
complete. Moreover, any vector of R^n+1 is performed by an energy-momentun
vector of one suitable metric of this family. They can in particular provide
counter-examples to the positive energy-momentum theorem when one removes the
completeness assumption.
