LEADER 04344nam 22006615 450 001 9910300253903321 005 20251116151520.0 010 $a1-4939-3246-2 024 7 $a10.1007/978-1-4939-3246-7 035 $a(CKB)3710000000498576 035 $a(EBL)4087165 035 $a(SSID)ssj0001585147 035 $a(PQKBManifestationID)16263049 035 $a(PQKBTitleCode)TC0001585147 035 $a(PQKBWorkID)14864553 035 $a(PQKB)11111494 035 $a(DE-He213)978-1-4939-3246-7 035 $a(MiAaPQ)EBC4087165 035 $a(PPN)189967706 035 $a(EXLCZ)993710000000498576 100 $a20151030d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeometry of hypersurfaces /$fby Thomas E. Cecil, Patrick J. Ryan 205 $a1st ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (601 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 08$a1-4939-3245-4 320 $aIncludes bibliographical references and index. 327 $aPreface -- 1. Introduction -- 2. Submanifolds of Real Space Forms -- 3. Isoparametric Hypersurfaces -- 4. Submanifolds in Lie Sphere Geometry -- 5. Dupin Hypersurfaces -- 6. Real Hypersurfaces in Complex Space Forms -- 7. Complex Submanifolds of CPn and CHn -- 8. Hopf Hypersurfaces -- 9. Hypersurfaces in Quaternionic Space Forms -- Appendix A. Summary of Notation -- References -- Index. 330 $aThis exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next comes a thorough treatment of the theory of real hypersurfaces in complex space forms. A central focus is a complete proof of the classification of Hopf hypersurfaces with constant principal curvatures due to Kimura and Berndt. The book concludes with the basic theory of real hypersurfaces in quaternionic space forms, including statements of the major classification results and directions for further research. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aGeometry, Differential 606 $aTopological groups 606 $aLie groups 606 $aGeometry, Hyperbolic 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aHyperbolic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21030 615 0$aGeometry, Differential. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aGeometry, Hyperbolic. 615 14$aDifferential Geometry. 615 24$aTopological Groups, Lie Groups. 615 24$aHyperbolic Geometry. 676 $a510 700 $aCecil$b Thomas E$4aut$4http://id.loc.gov/vocabulary/relators/aut$055379 702 $aRyan$b Patrick J.$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300253903321 996 $aGeometry of Hypersurfaces$92533261 997 $aUNINA