Articles liés à Topics in Extrinsic Geometry of Codimension-One Foliations
Synopsis
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.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
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Topics in Extrinsic Geometry of Codimension-One Foliations
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Springer New York, 2011
ISBN 10 : 1441999078
ISBN 13 : 9781441999078
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Kartoniert / Broschiert. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. New topic of foliation with a time-dependent metric is developedPresents new research tools in geometry of foliations (Extrinsic Geometric Flow)Presents examples and open problems for foliated surfacesExtrinsic geometry describ. N° de réf. du vendeur 4176821
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Topics in Extrinsic Geometry of Codimension-One Foliations (SpringerBriefs in Mathematics)
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Topics in Extrinsic Geometry of Codimension-One Foliations
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SPRINGER NATURE Jul 2011, 2011
ISBN 10 : 1441999078
ISBN 13 : 9781441999078
Neuf
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 114 pp. Englisch. N° de réf. du vendeur 9781441999078
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Topics in Extrinsic Geometry of Codimension-One Foliations (SpringerBriefs in Mathematics)
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9781441999078
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Topics in Extrinsic Geometry of Codimension - One Foliations
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Topics in Extrinsic Geometry of Codimension-One Foliations (SpringerBriefs in Mathematics)
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Topics in Extrinsic Geometry of Codimension-One Foliations
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Springer-Verlag New York Inc., 2011
ISBN 10 : 1441999078
ISBN 13 : 9781441999078
Neuf
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