{"product_id":"9781441999078","title":"SpringerBriefs in Mathematics","description":"\u003ch1\u003eSpringerBriefs in Mathematics\u003c\/h1\u003e \u003ch2\u003eRovenski, Vladimir; Walczak, Paweł\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eExtrinsic 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 \u003ci\u003eTopics in Extrinsic Geometry of Codimension-One\u003c\/i\u003e \u003ci\u003eFoliations\u003c\/i\u003e achieve a technical tour de force, which will lead to important geometric results. \u003c\/p\u003e\u003cp\u003e The \u003ci\u003eIntegral Formulae\u003c\/i\u003e, 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.\u003c\/p\u003e\u003cp\u003e\u003cb\u003e \u003c\/b\u003eThe central topic of this book is \u003ci\u003eExtrinsic Geometric Flow \u003c\/i\u003e(EGF) on foliated manifolds, which may be a tool for prescribing extrinsic geometric properties of foliations. To develop EGF, one needs \u003ci\u003eVariational Formulae\u003c\/i\u003e, 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 \u003ci\u003eExtrinsic Geometric Solutions\u003c\/i\u003e) of EGF are presented and are of great interest, since they provide Riemannian Structures with very particular geometry of the leaves.\u003c\/p\u003e\u003cp\u003e This work is aimed at those who have an interest in the differential geometry of submanifolds and foliations of Riemannian manifolds.    \u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2011-07-26\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781441999078\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4419-9908-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 114\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":45383176323212,"sku":"9781441999078","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781441999078.jpg?v=1775785733","url":"https:\/\/lateknightbooks.com\/products\/9781441999078","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}