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001 978-3-662-69721-4
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020 _a9783662697214
_9978-3-662-69721-4
024 7 _a10.1007/978-3-662-69721-4
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
072 7 _aPBMP
_2thema
100 1 _aKöhler, Kai.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986797
245 1 0 _aDifferential Geometry and Homogeneous Spaces
_h[electronic resource] /
_cby Kai Köhler.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aX, 292 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x2191-6675
505 0 _a1 Manifolds -- 2 Vector Bundles and Tensors -- 3 Riemannian Manifolds -- 4 The Poincaré–Hopf Theorem and the Chern–Gauß–Bonnet Theorem -- 5 Geodesics -- 6 Homogeneous Spaces -- 7 Symmetric Spaces -- 8 General Relativity -- A Solutions to Selected Exercises.
520 _aThis textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity. Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré–Hopf and Chern–Gauss–Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material. The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.
650 0 _aGeometry, Differential.
_969684
650 0 _aTopological groups.
_972299
650 0 _aLie groups.
_972300
650 0 _aMathematical physics.
650 1 4 _aDifferential Geometry.
_969686
650 2 4 _aTopological Groups and Lie Groups.
_972304
650 2 4 _aMathematical Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662697207
776 0 8 _iPrinted edition:
_z9783662697221
830 0 _aUniversitext,
_x2191-6675
_973095
856 4 0 _uhttps://doi.org/10.1007/978-3-662-69721-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c64588
_d64588