000			02349nam a22003257a 4500
003			OSt
005			20241112130136.0
008			241112b |||||||| |||| 00| 0 hin d
020			_a9783030890315
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a514.74 _bACA-T
100			_aA'Campo, Norbert
245			_aTopological, differential and conformal geometry of surfaces
260			_aSwitzerland : _bSpringer, _c2021
300			_ax, 284p. : _billustrations (chiefly color).
490			_aUniversitext _x0172-5939
504			_aIncludes bibliographical references and index
520			_aThis book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces.
521			_aBased on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
650			_aAlgebraic topology
650			_aGeometry, Algebraic
650			_aGeometry, Differential
650			_aGeometry, Riemannian
650			_aRiemann surface
650			_aHyperbolic geometry
650			_aTeichmuller space
856			_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-89032-2/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/61751984-topological-differential-and-conformal-geometry-of-surfaces?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cBK
999			_c35375 _d35375