000			03398nam a22004695i 4500
001			978-1-4419-9908-5
003			DE-He213
005			20140220083731.0
007			cr nn 008mamaa
008			110723s2011 xxu| s |||| 0|eng d
020			_a9781441999085 _9978-1-4419-9908-5
024	7		_a10.1007/978-1-4419-9908-5 _2doi
050		4	_aQA641-670
072		7	_aPBMP _2bicssc
072		7	_aMAT012030 _2bisacsh
082	0	4	_a516.36 _223
100	1		_aRovenski, Vladimir. _eauthor.
245	1	0	_aTopics in Extrinsic Geometry of Codimension-One Foliations _h[electronic resource] / _cby Vladimir Rovenski, Paweł Walczak.
250			_a1.
264		1	_aNew York, NY : _bSpringer New York, _c2011.
300			_aXV, 114p. 6 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringerBriefs in Mathematics, _x2191-8198
520			_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		0	_aMathematics.
650		0	_aDifferential equations, partial.
650		0	_aGlobal differential geometry.
650	1	4	_aMathematics.
650	2	4	_aDifferential Geometry.
650	2	4	_aPartial Differential Equations.
700	1		_aWalczak, Paweł. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441999078
830		0	_aSpringerBriefs in Mathematics, _x2191-8198
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4419-9908-5
912			_aZDB-2-SMA
999			_c106153 _d106153