000			03500nam a22004815i 4500
003			DE-He213
005			20191011041613.0
007			cr nn 008mamaa
008			110723s2011 xxu| s |||| 0|eng d
020	6	4	_a9781441999085 _9978-1-4419-9908-5
024	8	7	_a10.1007/978-1-4419-9908-5 _2doi
050	8	4	_aQA641-670
072	8	7	_aPBMP _2bicssc
072	8	7	_aMAT012030 _2bisacsh
082			_a516.36 _223
100	8	1	_aRovenski, Vladimir. _eauthor. _966942
245	9	7	_aTopics in Extrinsic Geometry of Codimension-One Foliations _h[electronic resource] / _cby Vladimir Rovenski, Pawe Walczak.
001			000053671
250	6	4	_a1.
300	6	4	_aXV, 114p. 6 illus. _bonline resource.
490	8	1	_aSpringerBriefs in Mathematics, _x2191-8198
520	6	4	_aExtrinsic 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.
650	8	0	_aMathematics. _98571
650	8	0	_aDifferential equations, partial. _99614
650	8	0	_aGlobal differential geometry. _99530
650			_aMathematics. _98571
650			_aDifferential Geometry. _99532
650			_aPartial Differential Equations. _99616
700	8	1	_aWalczak, Pawe. _eauthor. _966943
710	8	2	_aSpringerLink (Online service) _966944
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9781441999078
830	8	0	_aSpringerBriefs in Mathematics, _x2191-8198 _966945
856			_uhttp://dx.doi.org/10.1007/978-1-4419-9908-5 _zde clik aquí para ver el libro electrónico
264	8	1	_aNew York, NY : _bSpringer New York, _c2011.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
999			_c53401 _d53401
942			_c05