The study of Riemannian geometry is rather meaningless without some basic knowledge on Gaussian geometry i.e. The geometry of curves and surfaces in 3-dimensional Euclidean space. For this we recommend the following text: M. Do Carmo, Differential geometry.
With an additional structure, a (Riemannian) metric, and some important concepts we encounter are distance, geodesics, the Levi-Civita connection, and curvature.
Do Carmo, Riemannian Ge ometry, Birkh¨ auser (1992). I am very grateful to my man y enthusiastic studen ts who through- out the years hav e contributed to the text by finding n umerous typing. Orientation and Volume Forms 78 7. Notes on Chapter 2 80 Chapter 3. Riemannian Manifolds 87 1. Riemannian Manifolds 87 2. Affine Connections 94 3. Levi-Civita Connection 98 4. Minimizing Properties of Geodesics 104 5. How to download do carmo differential geometry solutions files to my device? Click download file button or Copy do carmo differential geometry solutions URL which shown in textarea when you clicked file title, and paste it into your browsers address bar. If file is multipart don't forget to check all parts before downloading! 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.
Mathematics: Theory & Applications
Authors: do Carmo, Manfredo Biopsychology 10 edition pdf.
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About this Textbook
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.
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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 into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.
Buy this book
Hardcover 41,55 €
Buy Hardcover
ISBN 978-0-8176-3490-2
Free shipping for individuals worldwide
Usually dispatched within 3 to 5 business days.
The final prices may differ from the prices shown due to specifics of VAT rules