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001			14924
009			197875416
003			http://www.sudoc.fr/197875416
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010			_a9780486806990 _bbr.
010			_a0-486-80699-5 _bbr.
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090			_a14924
099			_tOUVR _zALEX29748
100			_a20170126h20162016k y0frey50 ba
101	0		_aeng _2639-2
102			_aUS
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106			_ar
181			_6z01 _ctxt _2rdacontent
181		1	_6z01 _ai# _bxxxe##
182			_6z01 _cn _2rdamedia
182		1	_6z01 _an
183		1	_6z01 _anga _2RDAfrCarrier
200	1		_aDifferential geometry of curves & surfaces _fManfredo P. do Carmo,...
205			_aRevised & updated 2nd edition
214		0	_aMineola, New York _cDover Publications, Inc.
214		4	_dC 2016
215			_a1 vol. (XVI-510 p.) _cill., fig., graph. _d23 cm
320			_aBibliogr. p. 475-477. Index
330			_aLa 4e de couverture indique : "One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume"
359	1		_b1. Curves _cParametrized curves _cRegular curves; arc length _cThe vector product in R³ _cThe local theory of curves parametrized by arc length _cThe local canonical form _cGlobal properties of plane curves _b2. Regular surfaces _cRegular surfaces: inverse images of regular values _cChange of parameters: differential be functions on surface _cThe tangent plane: the differential of a map _cThe first fundamental form: area _cOrientation of surfaces _cA characterization of compact orientable surfaces _cA geometric definition of area _cAppendix: A brief review of continuity and differentiability _b3. The geometry of the Gauss map _cThe definition of the Gauss map and its fundamental properties _cThe Gauss map in local coordinates _cVector fields _cRuled surfaces and minimal surfaces _cAppendix: Self-adjoint linear maps and quadratic forms _b4. The intrinsic geometry of surfaces _cIsometrics: conformal maps _cThe Gauss theorem and the equations of compatibility _cParallel transport, Geodesics _cThe Gauss-Bonnet theorem and its applications _cThe exponential map. Geodesic polar coordinates _cFurther properties of geodesics: convex neighborhoods _cAppendix: Proofs of the fundamental theorems of the local theory of curves and surfaces _b5. Global differential geometry _cThe rigidity of the sphere _cComplete surfaces Theorem of Hopf-Rinow _cFirst and second variations of arc length: Bonnet's theorem _cJacobi fields and conjugate points _cCovering spaces: the theorems of Hadamard _cGlobal theorems for curves: the Fary-Milnor theorem _cSurfaces of zero Gaussian curvature _cJacobi's theorems _cAbstract surfaces: further generalizations _cHilbert's theorem _cAppendix: Point-set topology of Euclidean spaces
517			_aDifferential geometry of curves and surfaces
606			_aGeometry, Differential _2lc
606			_aCurves _2lc
606			_aSurfaces _2lc
606			_3027569918 _aGéométrie différentielle _2rameau
606			_3027355675 _aCourbes _2rameau
606			_3027586510 _aSurfaces (mathématiques) _2rameau
676			_a516.36 _v23
680			_aQA641 _b.C33 2016
686			_a53-01 _c2020 _2msc
686			_a53A05 _c2020 _2msc
686			_a53A10 _c2020 _2msc
686			_a53B20 _c2020 _2msc
686			_a53B25 _c2020 _2msc
686			_a53C20 _c2020 _2msc
686			_a53C40 _c2020 _2msc
686			_a53C45 _c2020 _2msc
700		1	_3032335687 _aCarmo _bManfredo Perdigão do _f1928-2018 _4070