<電子ブック>
Topics in Extrinsic Geometry of Codimension-One Foliations / by Vladimir Rovenski, Paweł Walczak
(SpringerBriefs in Mathematics. ISSN:21918201)
版 | 1st ed. 2011. |
---|---|
出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 2011 |
大きさ | XV, 114 p. 6 illus : online resource |
著者標目 | *Rovenski, Vladimir author Walczak, Paweł author SpringerLink (Online service) |
件 名 | LCSH:Geometry, Differential LCSH:Differential equations FREE:Differential Geometry FREE:Differential Equations |
一般注記 | 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. The Integral Formulae, introduced in chapter 1, is a useful for problems such as: prescribing higher mean curvatures of foliations, minimizing volume and energy defined for vector or plane fields on manifolds, and existence of foliations whose leaves enjoy given geometric properties. The Integral Formulae steams from a Reeb formula, for foliations on space forms which generalize the classical ones. For a special auxiliary functions the formulae involve the Newton transformations of the Weingarten operator. The central topic of this book is Extrinsic Geometric Flow (EGF) on foliated manifolds, which may be a tool for prescribing extrinsic geometric properties of foliations. To develop EGF, one needs Variational Formulae, revealed in chapter 2, which expresses a change in different extrinsic geometric quantities of a fixed foliation under leaf-wise variation of the Riemannian Structure of the ambient manifold. Chapter 3 defines a general notion of EGF and studies the evolution of Riemannian metrics along the trajectories of this flow(e.g., describes the short-time existence and uniqueness theory and estimate the maximal existence time).Some special solutions (called Extrinsic Geometric Solutions) of EGF are presented and are of great interest, since they provide Riemannian Structures with very particular geometry of the leaves. This work is aimed at those who have an interest in the differential geometry of submanifolds and foliations of Riemannian manifolds. HTTP:URL=https://doi.org/10.1007/978-1-4419-9908-5 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9781441999085 |
|
電子リソース |
|
EB00202057 |
類似資料
この資料の利用統計
このページへのアクセス回数:2回
※2017年9月4日以降