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An Introduction to Riemannian Geometry by C.E. Weatherburn

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About this book :-
An Introduction to Riemannian Geometry written by C.E. Weatherburn.
These lecture notes grew out of an M.Sc. course on differential geometry which the author gave at the University of Leeds 1992. Their main purpose is to introduce the beautiful theory of Riemannian Geometry a still very active research area of mathematics. This is a subject with no lack of interesting examples. They are indeed the key to a good understanding of it and will therefore play a major role throughout this work. Of special interest are the classical Lie groups allowing concrete calculations of many of the abstract notions on the menu.
The study of Riemannian Geometry is rather meaningless without some basic knowledge on Gaussian Geometry that is the differential geometry of curves and surfaces in 3-dimensional space. For this we recommend the excellent textbook: M. P. do Carmo, Differential geometry of curves and surfaces, Prentice Hall (1976).
These lecture notes are written for students with a good understanding of linear algebra, real analysis of several variables, the classical theory of ordinary differential equations and some topology. The most important results stated in the text are also proved there. Other smaller ones are left to the reader as exercises, which follow at the end of each chapter. This format is aimed at students willing to put hard work into the course.

Book Detail :-
Title: An Introduction to Riemannian Geometry
Edition:
Author(s): C.E. Weatherburn
Publisher: Cambridge University Press
Series:
Year: 2008
Pages: 92
Type: PDF
Language: Englsih
ISBN: 9780521091886,0521091888
Country: Astralia
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About Author :- Charles Ernest Weatherburn (1884–1974) was an Australian mathematician. Weatherburn graduated from the University of Sydney an MA in 1906. After being awarded a scholarship he studied at Trinity College, Cambridge sitting the Mathematical Tripos examinations in 1908. Weatherburn was awarded a First Class degree. On his return to Australia, Weatherburn taught at Ormond College of the University of Melbourne.
In 1923 was appointed chair of mathematics in Canterbury College, University of New Zealand. He returned to Australia in 1929 as chair of mathematics at the University of Western Australia, a post he held until he retired in 1950.

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Book Contents :-
An Introduction to Riemannian Geometry written by C.E. Weatherburn cover the following topics. '
1. Introduction
2. Differentiable Manifolds
3. The Tangent Space
4. The Tangent Bundle
5. Riemannian Manifolds
6. The Levi-Civita Connection
7. Geodesics
8. The Curvature Tensor
9. Curvature and Local Geometry


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