Matches in DBpedia 2016-04 for { <http://wikidata.dbpedia.org/resource/Q2502381> ?p ?o }
- Q2502381 subject Q8376419.
- Q2502381 abstract "In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss (articles of 1825 and 1827), who showed that curvature was an intrinsic property of a surface, independent of its isometric embedding in Euclidean space.Surfaces naturally arise as graphs of functions of a pair of variables, and sometimes appear in parametric form or as loci associated to space curves. An important role in their study has been played by Lie groups (in the spirit of the Erlangen program), namely the symmetry groups of the Euclidean plane, the sphere and the hyperbolic plane. These Lie groups can be used to describe surfaces of constant Gaussian curvature; they also provide an essential ingredient in the modern approach to intrinsic differential geometry through connections. On the other hand extrinsic properties relying on an embedding of a surface in Euclidean space have also been extensively studied. This is well illustrated by the non-linear Euler–Lagrange equations in the calculus of variations: although Euler developed the one variable equations to understand geodesics, defined independently of an embedding, one of Lagrange's main applications of the two variable equations was to minimal surfaces, a concept that can only be defined in terms of an embedding.".
- Q2502381 thumbnail Minimal_surface_curvature_planes-en.svg?width=300.
- Q2502381 wikiPageExternalLink E333.html.
- Q2502381 wikiPageExternalLink books?id=IQXstKvWsHMC&printsec=frontcover&dq=valiron+surfaces&source=gbs_summary_r&cad=0.
- Q2502381 wikiPageExternalLink digbib.cgi?PPN35283028X_0006_2NS.
- Q2502381 wikiPageExternalLink treatonthediffer00eiserich.
- Q2502381 wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0001.001.
- Q2502381 wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0002.001.
- Q2502381 wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0003.001.
- Q2502381 wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0004.001.
- Q2502381 wikiPageWikiLink Q10288828.
- Q2502381 wikiPageWikiLink Q1047080.
- Q2502381 wikiPageWikiLink Q1048874.
- Q2502381 wikiPageWikiLink Q1052034.
- Q2502381 wikiPageWikiLink Q10564970.
- Q2502381 wikiPageWikiLink Q1058314.
- Q2502381 wikiPageWikiLink Q1058681.
- Q2502381 wikiPageWikiLink Q1060372.
- Q2502381 wikiPageWikiLink Q1060874.
- Q2502381 wikiPageWikiLink Q1062978.
- Q2502381 wikiPageWikiLink Q106635.
- Q2502381 wikiPageWikiLink Q1071846.
- Q2502381 wikiPageWikiLink Q1072483.
- Q2502381 wikiPageWikiLink Q11352.
- Q2502381 wikiPageWikiLink Q1154082.
- Q2502381 wikiPageWikiLink Q1179296.
- Q2502381 wikiPageWikiLink Q1189065.
- Q2502381 wikiPageWikiLink Q124743.
- Q2502381 wikiPageWikiLink Q12507.
- Q2502381 wikiPageWikiLink Q1250766.
- Q2502381 wikiPageWikiLink Q12510.
- Q2502381 wikiPageWikiLink Q1256500.
- Q2502381 wikiPageWikiLink Q126017.
- Q2502381 wikiPageWikiLink Q127318.
- Q2502381 wikiPageWikiLink Q129199.
- Q2502381 wikiPageWikiLink Q1305766.
- Q2502381 wikiPageWikiLink Q1318998.
- Q2502381 wikiPageWikiLink Q1324364.
- Q2502381 wikiPageWikiLink Q1332643.
- Q2502381 wikiPageWikiLink Q1361396.
- Q2502381 wikiPageWikiLink Q1365281.
- Q2502381 wikiPageWikiLink Q1434805.
- Q2502381 wikiPageWikiLink Q1458609.
- Q2502381 wikiPageWikiLink Q146657.
- Q2502381 wikiPageWikiLink Q14851425.
- Q2502381 wikiPageWikiLink Q1491995.
- Q2502381 wikiPageWikiLink Q149972.
- Q2502381 wikiPageWikiLink Q1501536.
- Q2502381 wikiPageWikiLink Q154210.
- Q2502381 wikiPageWikiLink Q1545397.
- Q2502381 wikiPageWikiLink Q1589551.
- Q2502381 wikiPageWikiLink Q1614464.
- Q2502381 wikiPageWikiLink Q161973.
- Q2502381 wikiPageWikiLink Q162827.
- Q2502381 wikiPageWikiLink Q164321.
- Q2502381 wikiPageWikiLink Q164425.
- Q2502381 wikiPageWikiLink Q164784.
- Q2502381 wikiPageWikiLink Q1659965.
- Q2502381 wikiPageWikiLink Q1677714.
- Q2502381 wikiPageWikiLink Q1684673.
- Q2502381 wikiPageWikiLink Q16924.
- Q2502381 wikiPageWikiLink Q17091514.
- Q2502381 wikiPageWikiLink Q1715.
- Q2502381 wikiPageWikiLink Q17285.
- Q2502381 wikiPageWikiLink Q172937.
- Q2502381 wikiPageWikiLink Q17295.
- Q2502381 wikiPageWikiLink Q17502105.
- Q2502381 wikiPageWikiLink Q1754547.
- Q2502381 wikiPageWikiLink Q1783179.
- Q2502381 wikiPageWikiLink Q178546.
- Q2502381 wikiPageWikiLink Q1814838.
- Q2502381 wikiPageWikiLink Q186247.
- Q2502381 wikiPageWikiLink Q188444.
- Q2502381 wikiPageWikiLink Q188745.
- Q2502381 wikiPageWikiLink Q190109.
- Q2502381 wikiPageWikiLink Q190524.
- Q2502381 wikiPageWikiLink Q190546.
- Q2502381 wikiPageWikiLink Q193410.
- Q2502381 wikiPageWikiLink Q193657.
- Q2502381 wikiPageWikiLink Q1972021.
- Q2502381 wikiPageWikiLink Q1999772.
- Q2502381 wikiPageWikiLink Q202906.
- Q2502381 wikiPageWikiLink Q203920.
- Q2502381 wikiPageWikiLink Q206832.
- Q2502381 wikiPageWikiLink Q209306.
- Q2502381 wikiPageWikiLink Q2094241.
- Q2502381 wikiPageWikiLink Q2109761.
- Q2502381 wikiPageWikiLink Q213488.
- Q2502381 wikiPageWikiLink Q214159.
- Q2502381 wikiPageWikiLink Q214881.
- Q2502381 wikiPageWikiLink Q215067.
- Q2502381 wikiPageWikiLink Q215084.
- Q2502381 wikiPageWikiLink Q2152232.
- Q2502381 wikiPageWikiLink Q215964.
- Q2502381 wikiPageWikiLink Q216861.
- Q2502381 wikiPageWikiLink Q2184037.
- Q2502381 wikiPageWikiLink Q222032.
- Q2502381 wikiPageWikiLink Q2226643.
- Q2502381 wikiPageWikiLink Q2246553.