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About: Differential geometry of surfaces     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatSurfaces, within Data Space : dbpedia.org associated with source document(s)

Type: Thingyago:Artifact100021939yago:Object100002684yago:PhysicalEntity100001930yago:Surface104362025yago:Whole100003553yago:WikicatSurfaces New Facet based on Instances of this Class

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, who showed that curvature was an intrinsic property of a surface, independent of its isometric embedding in Euclidean space.