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Riemannian geometry by T. Sakai

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Published by American Mathematical Society in Providence, R.I .
Written in English

Subjects:

  • Geometry, Riemannian.

Book details:

Edition Notes

Includes bibliographical references and index.

StatementTakashi Sakai ; translated by Takashi Sakai.
SeriesTranslations of mathematical monographs ;, v. 149
Classifications
LC ClassificationsQA649 .S2513 1996
The Physical Object
Paginationxiii, 358 p. :
Number of Pages358
ID Numbers
Open LibraryOL969882M
ISBN 100821802844
LC Control Number96006475

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Lectures on Geodesics Riemannian Geometry. Aim of this book is to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it. Topics covered includes: Sprays, Linear connections, Riemannian manifolds, Geodesics, Canonical connection, Sectional Curvature and metric structure. “This is an introduction to modern methods in Riemannian geometry containing interesting and original approaches to many areas in this field. After a general introduction (metrics, curvature, geodesics) and concrete calculations for many examples, the second half of the book considers Bochner–Cartan techniques and comparison imeldaclyde.com: Springer-Verlag New York. I have studied differential geometry, and am looking for basic introductory texts on Riemannian geometry. My target is eventually Kähler geometry, but certain topics like geodesics, curvature, connections and transport belong more firmly in Riemmanian geometry. The reader can consult for instance the recent book [Br5]. of our “mentor” Marcel Berger. However, Riemannian Geometry is not only a fascinating field in itself. It has proved to be a precious tool in other parts of mathematics. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties.

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular. 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 imeldaclyde.com: Birkhäuser Basel. If you get a book about Riemannian geometry to precede a study of general relativity, you might be disappointed. Spacetime is pseudo-Riemannian. Once you get through your pure-math textbook.. you’ll have to revisit every single theorem to figure o. This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental /5(3).

Sep 23,  · 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/5(3). 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. Brand new Book. 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. Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry.