کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4606718 1337725 2006 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Ricci and Einstein equations on the pseudo-euclidean and hyperbolic spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On the Ricci and Einstein equations on the pseudo-euclidean and hyperbolic spaces
چکیده انگلیسی

We consider tensors T=fgT=fg on the pseudo-euclidean space RnRn and on the hyperbolic space HnHn, where n⩾3n⩾3, g is the standard metric and f   is a differentiable function. For such tensors, we consider, in both spaces, the problems of existence of a Riemannian metric g¯, conformal to g  , such that Ricg¯=T, and the existence of such a metric which satisfies Ricg¯−K¯g¯/2=T, where K¯ is the scalar curvature of g¯. We find the restrictions on the Ricci candidate for solvability and we construct the solutions g¯ when they exist. We show that these metrics are unique up to homothety, we characterize those globally defined and we determine the singularities for those which are not globally defined. None of the non-homothetic metrics g¯, defined on RnRn or HnHn, are complete. As a consequence of these results, we get positive solutions for the equation Δgu−n(n−2)4λu(n+2)(n−2)=0, where g is the pseudo-euclidean metric.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 24, Issue 2, March 2006, Pages 101–107
نویسندگان
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