LEADER 03888nam 2200517 450 001 996466481403316 005 20211211224940.0 010 $a3-540-39482-6 024 7 $a10.1007/3-540-39482-6 035 $a(CKB)3400000000100289 035 $a(DE-He213)978-3-540-39482-2 035 $a(MiAaPQ)EBC3072538 035 $a(MiAaPQ)EBC6575148 035 $a(Au-PeEL)EBL6575148 035 $a(OCoLC)1058913728 035 $a(PPN)155193880 035 $a(EXLCZ)993400000000100289 100 $a20211211d1989 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferential geometry in the large $eseminar lectures, New York University, 1946 and Stanford University, 1956 /$fHeinz Hopf 205 $a2nd ed. 1989. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer-Verlag,$d[1989] 210 4$d©1989 215 $a1 online resource (VIII, 192 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1000 311 $a3-540-51497-X 327 $aSelected Topics in Geometry -- The Euler Characteristic and Related Topics -- Selected Topics in Elementary Differential Geometry -- The Isoperimetric Inequality and Related Inequalities -- The Elementary Concept of Area and Volume -- Differential Geometry in the Large -- Differential Geometry of Surfaces in the Small -- Some General Remarks on Closed Surfaces in Differential Geometry -- The Total Curvature (Curvatura Inteqra) of a Closed Surface with Riemannian Metric and Poincaré?s Theorem on the Singularities of Fields of Line Elements -- Hadamard?s Characterization of the Ovaloids -- Closed Surfaces with Constant Gauss Curvature (Hilbert?s Method) ? Generalizations and Problems ? General Remarks on Weinqarten Surfaces -- General Closed Surfaces of Genus O with Constant Mean Curvature ? Generalizations -- Simple Closed Surfaces (of Arbitrary Genus) with Constant Mean Curvature ? Generalizations -- The Congruence Theorem for Ovaloids -- Singularities of Surfaces with Constant Negative Gauss Curvature. 330 $aThese notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, . 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1000 606 $aGeometry, Differential 606 $aGlobal differential geometry 615 0$aGeometry, Differential. 615 0$aGlobal differential geometry. 676 $a516.36 700 $aHopf$b Heinz$f1894-1971,$041921 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466481403316 996 $aDifferential geometry in the large$979959 997 $aUNISA