Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615622 | Journal of Mathematical Analysis and Applications | 2015 | 12 Pages |
Abstract
In the Euclidean space (Rn,g), with nâ¥3, gij=δij, we consider a diagonal (0,2)-tensor T=âifi(x)dxi2. We obtain necessary and sufficient conditions for the existence of a metric g¯, conformal to g, such that Ricg¯=T, where Ricg¯ is the Ricci curvature tensor of the metric g¯. The solution to this problem is given explicitly for special cases of the tensor T, including singular tensors and cases where the metric g¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Romildo Pina, Levi Adriano, Mauricio Pieterzack,