000 03375nam a22005295i 4500
001 978-3-031-02407-8
003 DE-He213
005 20240730163524.0
007 cr nn 008mamaa
008 220601s2015 sz | s |||| 0|eng d
020 _a9783031024078
_9978-3-031-02407-8
024 7 _a10.1007/978-3-031-02407-8
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
072 7 _aPB
_2thema
082 0 4 _a510
_223
100 1 _aGilkey, Peter.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_979024
245 1 0 _aAspects of Differential Geometry I
_h[electronic resource] /
_cby Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo.
250 _a1st ed. 2015.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXIII, 140 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Mathematics & Statistics,
_x1938-1751
505 0 _aPreface -- Acknowledgments -- Basic Notions and Concepts -- Manifolds -- Riemannian and Pseudo-Riemannian Geometry -- Bibliography -- Authors' Biographies -- Index .
520 _aDifferential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new. Table of Contents: Preface / Acknowledgments / Basic Notions and Concepts / Manifolds / Riemannian and Pseudo-Riemannian Geometry / Bibliography / Authors' Biographies / Index.
650 0 _aMathematics.
_911584
650 0 _aStatistics .
_931616
650 0 _aEngineering mathematics.
_93254
650 1 4 _aMathematics.
_911584
650 2 4 _aStatistics.
_914134
650 2 4 _aEngineering Mathematics.
_93254
700 1 _aPark, JeongHyeong.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_979025
700 1 _aVázquez-Lorenzo, Ramón.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_979026
710 2 _aSpringerLink (Online service)
_979027
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031012792
776 0 8 _iPrinted edition:
_z9783031035357
830 0 _aSynthesis Lectures on Mathematics & Statistics,
_x1938-1751
_979028
856 4 0 _uhttps://doi.org/10.1007/978-3-031-02407-8
912 _aZDB-2-SXSC
942 _cEBK
999 _c84700
_d84700