LEADER 03675nam 22006015 450 001 9910349346503321 005 20200706185246.0 010 $a1-4939-9644-4 024 7 $a10.1007/978-1-4939-9644-5 035 $a(CKB)4100000008878329 035 $a(DE-He213)978-1-4939-9644-5 035 $a(MiAaPQ)EBC5919106 035 $a(PPN)255066910 035 $a(EXLCZ)994100000008878329 100 $a20190802d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSubmanifold Theory $eBeyond an Introduction /$fby Marcos Dajczer, Ruy Tojeiro 205 $a1st ed. 2019. 210 1$aNew York, NY :$cSpringer US :$cImprint: Springer,$d2019. 215 $a1 online resource (XX, 628 p. 8 illus.) 225 1 $aUniversitext,$x0172-5939 311 $a1-4939-9642-8 327 $aThe basic equations of a submanifold -- Reduction of codimension -- Minimal submanifolds -- Local rigidity of submanifolds -- Constant curvature submanifolds -- Submanifolds with nonpositive extrinsic curvature -- Submanifolds with relative nullity -- Isometric immersions of Riemannian products -- Conformal immersions -- Isometric immersions of warped products -- The Sbrana-Cartan hypersurfaces -- Genuine deformations -- Deformations of complete submanifolds -- Innitesimal bendings -- Real Kaehler submanifolds -- Conformally at submanifolds -- Conformally deformable hypersurfaces -- Vector bundles. . 330 $aThis book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms. One main theme is the isometric and conformal deformation problem for submanifolds of arbitrary dimension and codimension. Several relevant classes of submanifolds are also discussed, including constant curvature submanifolds, submanifolds of nonpositive extrinsic curvature, conformally flat submanifolds and real Kaehler submanifolds. This is the first textbook to treat a substantial proportion of the material presented here. The first chapters are suitable for an introductory course on Submanifold theory for students with a basic background on Riemannian geometry. The remaining chapters could be used in a more advanced course by students aiming at initiating research on the subject, and are also intended to serve as a reference for specialists in the field. 410 0$aUniversitext,$x0172-5939 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aDifferential geometry 606 $aAlgebra 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aDifferential geometry. 615 0$aAlgebra. 615 14$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aDifferential Geometry. 615 24$aGeneral Algebraic Systems. 676 $a516.362 700 $aDajczer$b Marcos$4aut$4http://id.loc.gov/vocabulary/relators/aut$0782122 702 $aTojeiro$b Ruy$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349346503321 996 $aSubmanifold Theory$92529865 997 $aUNINA