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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Topics in Extrinsic Geometry of Codimension-One Foliations
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Topics in Extrinsic Geometry of Codimension-One Foliations
Vladimir Rovenski, Paweł Walczak (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.07.2011
Sprache
Englisch
EAN
9781441999078
Herausgeber
Springer US
Serien- oder Bandtitel
SpringerBriefs in Mathematics
Sonderedition
Nein
Autor
Vladimir Rovenski, Paweł Walczak
Seitenanzahl
114
Auflage
2011
Einbandart
Broschiert
Hersteller: Springer New York, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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