LEADER 04228nam 2200685Ia 450 001 9910453383203321 005 20200520144314.0 010 $a1-281-92492-X 010 $a9786611924928 010 $a981-277-371-1 035 $a(CKB)1000000000553151 035 $a(EBL)1214919 035 $a(SSID)ssj0000300309 035 $a(PQKBManifestationID)12071351 035 $a(PQKBTitleCode)TC0000300309 035 $a(PQKBWorkID)10252512 035 $a(PQKB)11743794 035 $a(MiAaPQ)EBC1214919 035 $a(WSP)00006095 035 $a(PPN)18136185X 035 $a(Au-PeEL)EBL1214919 035 $a(CaPaEBR)ebr10698886 035 $a(CaONFJC)MIL192492 035 $a(OCoLC)854973177 035 $a(EXLCZ)991000000000553151 100 $a20061027d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn introduction to Finsler geometry$b[electronic resource] /$fXiaohuan Mo 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2006 215 $a1 online resource (130 p.) 225 1 $aPeking University series in mathematics ;$vv. 1 300 $aDescription based upon print version of record. 311 $a981-256-793-3 320 $aIncludes bibliographical references (p. 117-118) and index. 327 $aPreface; Contents; 1 Finsler Manifolds; 1.1 Historical remarks; 1.2 Finsler manifolds; 1.3 Basic examples; 1.4 Fundamental invariants; 1.5 Reversible Finsler structures; 2 Geometric Quantities on a Minkowski Space; 2.1 The Cartan tensor; 2.2 The Cartan form and Deicke's Theorem; 2.3 Distortion; 2.4 Finsler submanifolds; 2.5 Imbedding problem of submanifolds; 3 Chern Connection; 3.1 The adapted frame on a Finsler bundle; 3.2 Construction of Chern connection; 3.3 Properties of Chern connection; 3.4 Horizontal and vertical subbundles of SM 327 $a4 Covariant Differentiation and Second Class of Geometric Invariants4.1 Horizontal and vertical covariant derivatives; 4.2 The covariant derivative along geodesic; 4.3 Landsberg curvature; 4.4 S-curvature; 5 Riemann Invariants and Variations of Arc Length; 5.1 Curvatures of Chern connection; 5.2 Flag curvature; 5.3 The first variation of arc length; 5.4 The second variation of arc length; 6 Geometry of Projective Sphere Bundle; 6.1 Riemannian connection and curvature of projective sphere bundle; 6.2 Integrable condition of Finsler bundle; 6.3 Minimal condition of Finsler bundle 327 $a7 Relation among Three Classes of Invariants7.1 The relation between Cartan tensor and flag curvature; 7.2 Ricci identities; 7.3 The relation between S-curvature and flag curvature; 7.4 Finsler manifolds with constant S-curvature; 8 Finsler Manifolds with Scalar Curvature; 8.1 Finsler manifolds with isotropic S-curvature; 8.2 Fundamental equation on Finsler manifolds with scalar curvature; 8.3 Finsler metrics with relatively isotropic mean Landsberg curvature; 9 Harmonic Maps from Finsler Manifolds; 9.1 Some definitions and lemmas; 9.2 The first variation; 9.3 Composition properties 327 $a9.4 The stress-energy tensor9.5 Harmonicity of the identity map; Bibliography; Index 330 $aThis introductory book uses the moving frame as a tool and develops Finsler geometry on the basis of the Chern connection and the projective sphere bundle. It systematically introduces three classes of geometrical invariants on Finsler manifolds and their intrinsic relations, analyzes local and global results from classic and modern Finsler geometry, and gives non-trivial examples of Finsler manifolds satisfying different curvature conditions. 410 0$aPeking University series in mathematics ;$vv. 1. 606 $aFinsler spaces 606 $aGeometry, Riemannian 606 $aManifolds (Mathematics) 608 $aElectronic books. 615 0$aFinsler spaces. 615 0$aGeometry, Riemannian. 615 0$aManifolds (Mathematics) 676 $a516.375 700 $aMo$b Xiao-huan$0943144 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453383203321 996 $aAn introduction to Finsler geometry$92128374 997 $aUNINA