LEADER 04651nam 2200673 a 450 001 9910824010003321 005 20240516164319.0 010 $a1-280-66899-7 010 $a9786613645920 010 $a1-84816-742-3 035 $a(CKB)2550000000101606 035 $a(EBL)919117 035 $a(OCoLC)794328410 035 $a(SSID)ssj0000656146 035 $a(PQKBManifestationID)12260718 035 $a(PQKBTitleCode)TC0000656146 035 $a(PQKBWorkID)10631498 035 $a(PQKB)10607642 035 $a(WSP)00002661 035 $a(Au-PeEL)EBL919117 035 $a(CaPaEBR)ebr10563518 035 $a(CaONFJC)MIL364592 035 $a(MiAaPQ)EBC919117 035 $a(EXLCZ)992550000000101606 100 $a20120608d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeometric realizations of curvature /$fMiguel Brozos Va?zquez, Peter B. Gilkey, Stana Nikcevic 205 $a1st ed. 210 $aLondon $cImperial College Press$d2012 215 $a1 online resource (263 p.) 225 1 $aICP advanced texts in mathematics,$x1753-657X ;$vv. 6 300 $aDescription based upon print version of record. 311 $a1-84816-741-5 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1. Introduction and Statement of Results; 1.1 Notational Conventions; 1.2 Representation Theory; 1.3 Affine Structures; 1.4 Mixed Structures; 1.5 Affine Kahler Structures; 1.6 Riemannian Structures; 1.7 Weyl Geometry I; 1.8 Almost Pseudo-Hermitian Geometry; 1.9 The Gray Identity; 1.10 Kahler Geometry in the Riemannian Setting I; 1.11 Curvature Kahler-Weyl Geometry; 1.12 The Covariant Derivative of the Kahler Form I; 1.13 Hyper-Hermitian Geometry; 2. Representation Theory; 2.1 Modules for a Group G; 2.2 Quadratic Invariants; 2.3 Weyl's Theory of Invariants 327 $a2.4 Some Orthogonal Modules2.5 Some Unitary Modules; 2.6 Compact Lie Groups; 3. Connections, Curvature, and Differential Geometry; 3.1 Affine Connections; 3.2 Equiaffine Connections; 3.3 The Levi-Civita Connection; 3.4 Complex Geometry; 3.5 The Gray Identity; 3.6 Kahler Geometry in the Riemannian Setting II; 4. Real Affine Geometry; 4.1 Decomposition of and as Orthogonal Modules; 4.2 The Modules R, S2 0 , and ?2 in; 4.3 The Modules WO6 , WO7 , and WO8 in; 4.4 Decomposition of as a General Linear Module; 4.5 Geometric Realizability of Affine Curvature Operators 327 $a4.6 Decomposition of as an Orthogonal Module5. Affine Kahler Geometry; 5.1 Affine Kahler Curvature Tensor Quadratic Invariants; 5.2 The Ricci Tensor for a Kahler Affine Connection; 5.3 Constructing Affine (Para)-Kahler Manifolds; 5.4 Affine Kahler Curvature Operators; 5.5 Affine Para-Kahler Curvature Operators; 5.6 Structure of as a GL Module; 6. Riemannian Geometry; 6.1 The Riemann Curvature Tensor; 6.2 The Weyl Conformal Curvature Tensor; 6.3 The Cauchy-Kovalevskaya Theorem; 6.4 Geometric Realizations of Riemann Curvature Tensors; 6.5 Weyl Geometry II; 7. Complex Riemannian Geometry 327 $a7.1 The Decomposition of as Modules over7.2 The Submodules of Arising from the Ricci Tensors; 7.3 Para-Hermitian and Pseudo-Hermitian Geometry; 7.4 Almost Para-Hermitian and Almost Pseudo-Hermitian Geometry; 7.5 Kahler Geometry in the Riemannian Setting III; 7.6 Complex Weyl Geometry; 7.7 The Covariant Derivative of the Kahler Form II; Notational Conventions; Bibliography; Index 330 $aA central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing ont 410 0$aImperial College Press advanced texts in mathematics ;$vv. 6. 606 $aCurvature 606 $aGeometry 615 0$aCurvature. 615 0$aGeometry. 676 $a516 700 $aBrozos-Va?zquez$b Miguel$0785012 701 $aGilkey$b Peter B$061410 701 $aNikcevic$b Stana$01611863 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910824010003321 996 $aGeometric realizations of curvature$93940323 997 $aUNINA