Extrinsic geometric flows on foliated manifolds, III

Details Extrinsic geometric flows on foliated manifolds, III Extrinsic geometric flows on foliated manifolds, III

2011-08-25

arxiv.org/abs/1108.5071v2

Mathematics

Differential Geometry

20 pages

Scientific paper

We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies along the leaves of the foliation. Then the Extrinsic Geometric Flow depending on the second fundamental form of the foliation is introduced. Under suitable assumptions, this evolution yields the second order parabolic PDEs, for which the existence/uniquenes and in some cases convergence of a solution are shown. Applications to the problem of prescribing mean curvature function of a codimension-one foliation, and examples with harmonic and umbilical foliations (e.g., foliated surfaces) and with twisted product metrics are given.

Affiliated with

Also associated with

No associations

Rating

Extrinsic geometric flows on foliated manifolds, III 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 Extrinsic geometric flows on foliated manifolds, III, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extrinsic geometric flows on foliated manifolds, III will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-319091