Mathematics – Differential Geometry
Scientific paper
2010-10-14
Mathematics
Differential Geometry
20 pages
Scientific paper
We consider a problem of prescribing the partial Ricci curvature on a locally conformally flat manifold $(M^n, g)$ endowed with the complementary orthogonal distributions $D_1$ and $D_2$. We provide conditions for symmetric $(0,2)$-tensors $T$ of a simple form (defined on $M$) to admit metrics $\tilde g$, conformal to $g$, that solve the partial Ricci equations. The solutions are given explicitly. Using above solutions, we also give examples to the problem of prescribing the mixed scalar curvature related to $D_i$. In aim to find "optimally placed" distributions, we calculate the variations of the total mixed scalar curvature (where again the partial Ricci curvature plays a key role), and give examples concerning minimization of a total energy and bending of a distribution.
No associations
LandOfFree
On the partial Ricci curvature of foliations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the partial Ricci curvature of foliations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the partial Ricci curvature of foliations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-286277