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DIFFERENTIAL SURFACES - فدیکا

DIFFERENTIAL GEOMETRYOFCURVES & SURFACESDIFFERENTIAL GEOMETRYOFCURVES & SURFACESR evised & Updated SECOND EDITIONM anfredo P. do CarmoInstituto Nacional de Matem tica Pura e Aplicada (IMPA)Rio de Janeiro, BrazilDOVER PUBLICATIONS, , New YorkCopyrightCopyright 1976, 2016 by Manfredo P. do CarmoAll rights Note DIFFERENTIAL Geometry of Curves and SURFACES : Revised & Updated Second Edition is a revised, corrected, and updated second edition of the work originally published in 1976 by Prentice-Hall, Inc., Englewood Cliffs, New Jersey. The author has also provided a new Preface for this Standard Book NumberISBN-13: 978-0-486-80699-0 ISBN-10: 0-486-80699-5 Manufactured in the United States by LSC Communications80699501 Leny,for her indispensable assistancein all the stages of this bookContentsPreface to the Second Edition xiPreface xiiiSome Remarks on Using this Book xv1.

4-3 The Gauss Theorem and the Equations of Compatibility 235 4-4 Parallel Transport. Geodesics. 241 4-5 The Gauss-Bonnet Theorem and ItsApplications 267 4-6 The Exponential Map. Geodesic Polar Coordinates 287 4-7 Further Properties of Geodesics; Convex Neighborhoods 302 Appendix: Proofs of the Fundamental Theorems of the Local Theory of …

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