Extrinsic geometric flows on foliated manifolds, I

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

2010-03-08

arxiv.org/abs/1003.1607v3

Mathematics

Differential Geometry

34 pages, 2 figures

Scientific paper

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.

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