Synopses & Reviews
Extrinsic geometry describes properties of foliations on Riemannian manifolds which can be expressed in terms of the second fundamental form of the leaves. The authors of Topics in Extrinsic Geometry of Codimension-One Foliations achieve a technical tour de force, which will lead to important geometric results.
Review
From the reviews: "There are three chapters in this research monograph, each devoted to a different aspect of the extrinsic geometry of Ƒ. ... This book generalizes well-known results but also covers new ground. It is rich in ideas for those who are interested in the geometry of codimension-one foliations." (James Hebda, Zentralblatt MATH, Vol. 1228, 2012)
Synopsis
Extrinsic geometry describes those properties of foliations on Riemannian manifolds which can be expressed in terms of the second fundamental form of the leaves. The central topic of this book is Extrinsic Geometric Flow (EGF) on foliated manifolds.
Table of Contents
-1. Integral Formulae (Introduction, Preliminaries, Integral Formulae for Codimension-one foliations).-2.Variation Formulae (Introduction, Auxiliary results, Variations of extrinsic geometric quantities, Variations of general functional, Variations of particular functional, Applications and examples).-3. Extrinsic Geometric Flows (Introduction, The systems of PDE's related to EGF, Auxiliary results, Existence and uniqueness results, A solution to general case, Global existence of EGF, Variation formulae for EGF, Extrinsic geometric solitons, Applications and examples).- References.