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Riemannian geometry / Manfredo Perdigäao do Carmo ; translated by Francis Flaherty.

By: Carmo, Manfredo Perdigão do.
Material type: materialTypeLabelBookSeries: Mathematics (Boston, Mass.).Publisher: Boston : Birkhauser, c1992Description: 300 p. : ill. ; 25 cm. + hbk.ISBN: 0817634908 ; 3764334908 .Subject(s): Geometry, RiemannianDDC classification: 516.373
Contents:
0-Differentiable manifolds -- Riemannian metrics -- Affine connections; Riemannian connections -- Geodesics; convex neighborhoods -- Curvature -- Jacobi fields -- Isometric immersions -- Complete manifolds; Hopp-Rinow and Hadamard theorems -- Spaces of constant curvature -- Variations of energy -- The Rauch comparison theorem -- The morse index theorem -- The fundamental group of manifolds of negative curvature -- The sphere theorem.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 516.373 (Browse shelf(Opens below)) 1 Available 00016974
Total holds: 0

Enhanced descriptions from Syndetics:

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.

A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight intothe subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.

Mathematics, theory & applications.

Includes bibliographical references (pages 292-296) and index.

0-Differentiable manifolds -- Riemannian metrics -- Affine connections; Riemannian connections -- Geodesics; convex neighborhoods -- Curvature -- Jacobi fields -- Isometric immersions -- Complete manifolds; Hopp-Rinow and Hadamard theorems -- Spaces of constant curvature -- Variations of energy -- The Rauch comparison theorem -- The morse index theorem -- The fundamental group of manifolds of negative curvature -- The sphere theorem.

Translation the 2nd ed. of: Geometria riemanniana.

Table of contents provided by Syndetics

  • Preface to the 1st edition
  • Preface to the 2nd edition
  • Preface to the English edition
  • How to use this book
  • 0 Differentiable Manifolds
  • 1 Riemannian Metrics
  • 2 Affine Connections
  • Riemannian Connections
  • 3 Geodesics
  • Convex Neighborhoods
  • 4 Curvature
  • 5 Jacobi Fields
  • 6 Isometric Immersions
  • 7 Complete Manifolds
  • Hopf-Rinow and Hadamard Theorems
  • 8 Spaces of Constant Curvature
  • 9 Variations of Energy
  • 10 The Rauch Comparison Theorem
  • 11 The Morse Index Theorem
  • 12 The Fundamental Group of Manifolds of Negative Curvature
  • 13 The Sphere Theorem
  • References
  • Index

Reviews provided by Syndetics

CHOICE Review

Differential geometry is a beautifully elegant subject that is also uncompromisingly technical in its language. This book is a translation from the Portuguese of the second edition of the author's Geometria Riemanniana (Rio de Janeiro, Brazil, 1988) and is appropriate for graduate students studying the techniques and fundamental theorems of Riemannian geometry. In his presentation, Do Carmo effectively strikes a delicate balance between the Byzantine nature of local coordinate computations and the stark austerity of the more modern invariant approach to differential geometry. The result is a solid, readable (though demanding) book full of wonderful mathematical taste. Exercises abound and there is an extensive bibliography. No doubt destined to become a standard reference in the field. Highly recommended for advanced undergraduates, graduate students, and professionals.-S. J. Colley, Oberlin College