LEADER 03898nam 2200625Ia 450 001 9910454406803321 005 20200520144314.0 010 $a9786611960650 010 $a1-281-96065-9 010 $a981-281-162-1 035 $a(CKB)1000000000538059 035 $a(StDuBDS)AH24685634 035 $a(SSID)ssj0000190861 035 $a(PQKBManifestationID)11190023 035 $a(PQKBTitleCode)TC0000190861 035 $a(PQKBWorkID)10180952 035 $a(PQKB)10381948 035 $a(MiAaPQ)EBC1681622 035 $a(WSP)00004619 035 $a(Au-PeEL)EBL1681622 035 $a(CaPaEBR)ebr10256005 035 $a(CaONFJC)MIL196065 035 $a(OCoLC)815756559 035 $a(EXLCZ)991000000000538059 100 $a20010817d2001 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Finsler geometry$b[electronic resource] /$fZhongmin Shen 210 $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$d2001 215 $a1 online resource (324p.) 225 0$aSeries on Multivariate Analysis 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-02-4531-9 311 $a981-02-4530-0 320 $aIncludes bibliographical references (p. 299-304) and index. 327 $aFinsler Spaces; Finsler m Spaces; Co-Area Formula; Isoperimetric Inequalities; Geodesics and Connection; Riemann Curvature; Non-Riemannian Curvatures; Structure Equations; Finsler Spaces of Constant Curvature; Second Variation Formula; Geodesics and Exponential Map; Conjugate Radius and Injectivity Radius; Basic Comparison Theorems; Geometry of Hypersurfaces; Geometry of Metric Spheres; Volume Comparison Theorems; Morse Theory of Loop Spaces; Vanishing Theorems for Homotopy Groups; Spaces of Finsler Spaces. 330 $aViewing Finsler spaces as regular metric spaces, this work discusses the problems from the modern metric geometry point of view. It addresses the basics on Finsler spaces, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory. 330 $bIn 1854, B. Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 1918, when P. Finsler studied the variation problem in regular metric spaces. Around 1926, L. Berwald extended Riemann's notion of curvature to regular metric spaces and introduced an important non-Riemannian curvature using his connection for regular metrics. Since then, Finsler geometry has developed steadily. In his Paris address in 1900, D. Hilbert formulated 23 problems, the 4th and 23rd problems being in Finsler's category. Finsler geometry has broader applications in many areas of science and will continue to develop through the efforts of many geometers around the world.;Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern geometry point of view. The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory. 606 $aFinsler spaces 606 $aGeometry, Differential 608 $aElectronic books. 615 0$aFinsler spaces. 615 0$aGeometry, Differential. 676 $a516.375 700 $aShen$b Zhongmin$f1963-$061117 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454406803321 996 $aLectures on finsler geometry$9377022 997 $aUNINA