LEADER 04035nam 22006495 450 001 9910483832803321 005 20251202143256.0 010 $a3-030-46047-9 024 7 $a10.1007/978-3-030-46047-1 035 $a(CKB)4100000011389994 035 $a(DE-He213)978-3-030-46047-1 035 $a(MiAaPQ)EBC6455979 035 $a(MiAaPQ)EBC6308759 035 $a(Au-PeEL)EBL6308759 035 $a(OCoLC)1187169134 035 $a(PPN)25021525X 035 $a(EXLCZ)994100000011389994 100 $a20200817d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferential Geometry and Lie Groups $eA Second Course /$fby Jean Gallier, Jocelyn Quaintance 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XIV, 620 p. 110 illus., 32 illus. in color.) 225 1 $aGeometry and Computing,$x1866-6809 ;$v13 311 08$a3-030-46046-0 327 $a1. Tensor Algebras -- 2. Exterior Tensor Powers and Exterior Algebras -- 3. Differential Forms -- 4. Distributions and the Frobenius Theorem -- 5. Integration on Manifolds -- 6. Spherical Harmonics and Linear Representations -- 7. Operators on Riemannian Manifolds -- 8. Bundles, Metrics on Bundles, Homogeneous Spaces -- 9. Connections and Curvature in Vector Bundles -- 10. Clifford Algebras, Clifford Groups, Pin and Spin. 330 $aThis textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraicconclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors? companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation. 410 0$aGeometry and Computing,$x1866-6809 ;$v13 606 $aGeometry, Differential 606 $aTopological groups 606 $aLie groups 606 $aMathematics$xData processing 606 $aDifferential Geometry 606 $aTopological Groups and Lie Groups 606 $aComputational Mathematics and Numerical Analysis 615 0$aGeometry, Differential. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aMathematics$xData processing. 615 14$aDifferential Geometry. 615 24$aTopological Groups and Lie Groups. 615 24$aComputational Mathematics and Numerical Analysis. 676 $a516.36 676 $a516.36 700 $aGallier$b Jean H.$065693 702 $aQuaintance$b Jocelyn 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483832803321 996 $aDifferential geometry and lie groups$91886071 997 $aUNINA