LEADER 03196nam 22005655 450 001 9910483160303321 005 20251107152432.0 010 $a3-030-70067-4 024 7 $a10.1007/978-3-030-70067-6 035 $a(CKB)4100000011946519 035 $a(MiAaPQ)EBC6629005 035 $a(Au-PeEL)EBL6629005 035 $a(OCoLC)1255219949 035 $a(PPN)25588205X 035 $a(DE-He213)978-3-030-70067-6 035 $a(EXLCZ)994100000011946519 100 $a20210522d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExtrinsic Geometry of Foliations /$fby Vladimir Rovenski, Pawe? Walczak 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (327 pages) 225 1 $aProgress in Mathematics,$x2296-505X ;$v339 311 08$a3-030-70066-6 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1. Preliminaries -- 2. Integral formulas -- 3. Prescribing the mean curvature -- 4. Variational formulae -- 5. Extrinsic Geometric flows -- References -- Index. 330 $aThis book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well asexperienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore. 410 0$aProgress in Mathematics,$x2296-505X ;$v339 606 $aGeometry, Differential 606 $aManifolds (Mathematics) 606 $aDifferential Geometry 606 $aManifolds and Cell Complexes 615 0$aGeometry, Differential. 615 0$aManifolds (Mathematics) 615 14$aDifferential Geometry. 615 24$aManifolds and Cell Complexes. 676 $a514.72 700 $aRovenskii$b Vladimir Y.$f1953-$01076104 702 $aWalczak$b Pawe? Grzegorz 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483160303321 996 $aExtrinsic geometry of foliations$92586223 997 $aUNINA