LEADER 03541nam 2200529 450 001 9910483832803321 005 20211005215051.0 010 $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 $a20210406d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDifferential geometry and lie groups $ea second course /$fJean Gallier, Jocelyn Quaintance 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (XIV, 620 p. 110 illus., 32 illus. in color.) 225 1 $aGeometry and computing ;$vVolume 13 311 $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 $aThis textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors? companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation. 410 0$aGeometry and computing ;$vVolume 13. 606 $aGeometry, Differential 606 $aTopological groups 615 0$aGeometry, Differential. 615 0$aTopological groups. 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