Transcription of Introduction to Differential Geometry General Relativity
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Introduction to Differential Geometry General Relativity
Introduction to Differential Geometry & General Relativity 6th Printing May 2014 Lecture Notes by Stefan Waner with a Special Guest Lecture by Gregory C. Levine Departments of Mathematics and Physics, Hofstra University 2 Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, with a Special Guest Lecture by Gregory C. Levine Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries ..3 2. Smooth Manifolds and Scalar Fields ..8 3. Tangent Vectors and the Tangent Space ..16 4. Contravariant and Covariant Vector Fields ..26 5. Tensor Fields ..37 6. Riemannian Manifolds ..42 7. Locally Minkowskian Manifolds: An Introduction to Relativity ..52 8. Covariant Differentiation ..63 9. Geodesics and Local Inertial Frames ..71 10. The Riemann Curvature Tensor ..83 11. A Little More Relativity : Comoving Frames and Proper Time.
Introduction to Differential Geometry & General Relativity 6th Printing May 2014 Lecture Notes by Stefan Waner with a Special Guest Lecture by Gregory C. Levine Departments of Mathematics and Physics, Hofstra University
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