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5 Mb, about 200 pages, Last Updated: January, 2002 2002

Abstract:

An introductory book on Differential Geometry and General Relativity, combined, with mathematics presented first at an accessible level. Lecture 8: Covariant Differentiation; Lecture 10: The Riemann Curvature Tensor; Lecture 9: Geodesics and Local Inertial Frames http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html Introduction to Differential Geometry and General Relativity "Lecture Notes by Stefan Waner, Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields 5. Tensor Fields 6. Riemannian Manifolds 7. Locally Minkowskian Manifolds: A Little Relativity 8. Covariant Differentiation 9. Geodesics and Local Inertial Frames 10. The Riemann Curvature Tensor 11. A Little More Relativity: Comoving Frames and Proper Time 12. The Stress Tensor and the Relativistic Stress-Energy Tensor 13. Three Basic Premises of General Relativity 14. The Einstein Field Equations and Derivation of Newton's Law 15. The Schwarzschild Metric and Event Horizons 16. White Dwarfs, Neutron Stars and Black Holes by Gregory C. Levine Download the latest version of the differential geometry/relativity notes in PDF format. References and Suggested Further Reading (Listed in the rough order reflecting the degree to which they were used) Bernard F. Schutz, A First Course in General Relativity (Cambridge University Press, 1986) David Lovelock and Hanno Rund, Tensors, Differential Forms, and Variational Principles (Dover, 1989) Charles E. Weatherburn, An Introduction to Riemannian Geometry and the Tensor Calculus (Cambridge University Press, 1963) Charles W. Misner, Kip S. Thorne and John A. Wheeler, Gravitation (W.H. Freeman, 1973) Keith R. Symon, Mechanics (3rd. Ed. Addison Wesley) "Further Reading on the Web : For a comprehensive catalog of internet sites on special and general relativity, visit Relativity on the Web."

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open access: http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html Copyright@2002 by Stefan Waner

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