2010/03/08 by Vladimir Rovenski, Rovenski, Vladimir, Paweł Walczak +2
Mathematics · #Mathematical Dynamics and Fractals #math.DG #msc:35L45 #msc:53C12 #msc:58J45
paper · pdf · doi:10.48550/arxiv.1003.1607
34 pages, 2 figures
arxiv created 2011/08/14 · arxiv updated 2011/08/16
We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. We prove the local existence and uniqueness theorem and estimate the existence time of solutions for some particular cases. The key step of the solution procedure is to find (from a system of quasilinear PDE's) the principal curvatures of the foliation. Examples for extrinsic Newton transformation flow, extrinsic Ricci flow, and applications to foliations on surfaces are given.