000 04006nam a22004695i 4500
001 978-3-540-39482-2
003 DE-He213
005 20190213151134.0
007 cr nn 008mamaa
008 121227s1989 gw | s |||| 0|eng d
020 _a9783540394822
_9978-3-540-39482-2
024 7 _a10.1007/3-540-39482-6
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
072 7 _aPBMP
_2thema
082 0 4 _a516.36
_223
100 1 _aHopf, Heinz.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aDifferential Geometry in the Large
_h[electronic resource] :
_bSeminar Lectures New York University 1946 and Stanford University 1956 /
_cby Heinz Hopf.
250 _aSecond Edition.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1989.
300 _aVIII, 192 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1000
505 0 _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.
520 _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, .
650 0 _aGlobal differential geometry.
650 1 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540514978
776 0 8 _iPrinted edition:
_z9783662210925
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1000
856 4 0 _uhttps://doi.org/10.1007/3-540-39482-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9649
_d9649