کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1894595 1044208 2007 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A class of solutions of the Ricci and Einstein equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
A class of solutions of the Ricci and Einstein equations
چکیده انگلیسی

We consider the pseudo-Euclidean space (Rn,g)(Rn,g), with n≥3n≥3 and gij=δijϵigij=δijϵi, ϵi=±1ϵi=±1 and tensors of the form T=∑ifi(xk)ϵidxi2 for a fixed kk, 1≤k≤n1≤k≤n. We provide necessary and sufficient conditions for such a tensor to admit metrics ḡ, conformal to gg, that solve the Ricci equation or the Einstein equation. The solution to this problem is given explicitly and it depends on an arbitrary differentiable function of one variable. Similar problems are considered for locally conformally flat manifolds. Examples are provided of complete metrics on RnRn, whose Ricci curvature is negative. Complete metrics are also given on the cylinder or on the nn-dimensional torus, that solve the Ricci equation or the Einstein equation. Examples of metrics with positive Ricci curvatures are given on half-spaces of RnRn.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 57, Issue 3, February 2007, Pages 881–888
نویسندگان
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