LEADER 03315nam 22005655 450 001 9910964624503321 005 20250811094752.0 010 $a3-662-02897-2 024 7 $a10.1007/978-3-662-02897-1 035 $a(CKB)2660000000026955 035 $a(SSID)ssj0001296914 035 $a(PQKBManifestationID)11709196 035 $a(PQKBTitleCode)TC0001296914 035 $a(PQKBWorkID)11353919 035 $a(PQKB)11584256 035 $a(DE-He213)978-3-662-02897-1 035 $a(MiAaPQ)EBC3097862 035 $a(PPN)238018784 035 $a(EXLCZ)992660000000026955 100 $a20130125d1993 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGeometry IV $eNon-regular Riemannian Geometry /$fedited by Yu.G. Reshetnyak 205 $a1st ed. 1993. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1993. 215 $a1 online resource (VII, 252 p.) 225 1 $aEncyclopaedia of Mathematical Sciences ;$v70 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-54701-0 311 08$a3-642-08125-8 320 $aIncludes bibliographical references at the end of each chapters and indexes. 327 $aI. Two-Dimensional Manifolds of Bounded Curvature -- II. Multidimensional Generalized Riemannian Spaces -- Author Index. 330 $aThe book contains a survey of research on non-regular Riemannian geome­ try, carried out mainly by Soviet authors. The beginning of this direction oc­ curred in the works of A. D. Aleksandrov on the intrinsic geometry of convex surfaces. For an arbitrary surface F, as is known, all those concepts that can be defined and facts that can be established by measuring the lengths of curves on the surface relate to intrinsic geometry. In the case considered in differential is defined by specifying its first geometry the intrinsic geometry of a surface fundamental form. If the surface F is non-regular, then instead of this form it is convenient to use the metric PF' defined as follows. For arbitrary points X, Y E F, PF(X, Y) is the greatest lower bound of the lengths of curves on the surface F joining the points X and Y. Specification of the metric PF uniquely determines the lengths of curves on the surface, and hence its intrinsic geometry. According to what we have said, the main object of research then appears as a metric space such that any two points of it can be joined by a curve of finite length, and the distance between them is equal to the greatest lower bound of the lengths of such curves. Spaces satisfying this condition are called spaces with intrinsic metric. Next we introduce metric spaces with intrinsic metric satisfying in one form or another the condition that the curvature is bounded. 410 0$aEncyclopaedia of Mathematical Sciences ;$v70 606 $aGeometry, Differential 606 $aDifferential Geometry 615 0$aGeometry, Differential. 615 14$aDifferential Geometry. 676 $a516.36 702 $aReshetnyak$b Yu.G$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910964624503321 996 $aGeometry IV$979767 997 $aUNINA