Course: MIT OPEN COURSEWARE
- Discrete Diferential Geometry of Curves and Surfaces.pdf – Tim Hofmann
- Lectures on the Differential Geometry of Curves and Surfaces.pdf Paul A. Blaga
- Lecture Notes on Differential Geometry – Mohammad Ghomi
Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics) 2nd Edition, by
First Steps in Differential Geometry: Riemannian, Contact, Symplectic (Undergraduate Texts in Mathematics) 2013th Edition, by
- Foundations of Differentiable manifolds and Lie groups, Frank Warner
- Calculus on Manifolds.pdf, Micheal Spivak
- Differential Geometry and Symmetric Space, Singurdur Helgason.
- Mathematical Methods of Classical Mechanics, V.I. Arnold.
- Gauge Fields, Knots, and Gravity, John C. Baez.
(Differential geometry in applied mathematics and in physics)
(with introduction to tensor calculus)
Differential Forms and Applications (Universitext) 1st ed. 1994. Corr. 2nd printing 1998 Edition, by
- Differential Geometry of Curves and Surfaces.pdf by Manredo P. do Carmo
Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics) (v. 94), by
- What are the differences between Differential Topology, Differential Geometry, Algebraic Topology, and Algebraic Geometry?
- Geometry Processing Algorithms – Differential Geometry
Math Differential Geometry
Math 352 Bard College
Math 561 – The Differential Geometry of Curves and Surfaces
- Some lecture notes on Curves based on the first chapter of do Carmo’s textbook.
- Solutions to some problems from the first chapter of the do Carmo’s textbook.
- More solutions to problems from the first chapter of the do Carmo’s textbook.
- Some lecture notes on surfaces base on the second chapter of do Carmo’s textbook.
- Solutions to some problems from the second chapter of do Carmo’s textbook.
- An elementary proof that stereographic projection is conformal and another copy of this document.
- An online book on differential geometry which I like better than the Do Carmo textbook. In this book there is a careful statement of the Inverse and Implicit Function Theorems on page 3 and a proof that the three definitions of a regular surface are equivalent on page 6.
- Some lecture notes on the Gauss map based on the third chapter of do Carmo’s textbook.
- Some lecture notes on manifolds and maps that I used whenever I taught Math 761.
Kinematic Differential Geometry and Saddle Synthesis of Linkages
- Computational Manifolds and Applications
- Advanced Geometric Methods in Computer Science
- Basic of Algebra, Topology, and Differential Calculus.pdf
- Algebraic Geometry
- Introduction to Discrete Probability
- All books http://www.cis.upenn.edu/~jean/gbooks/home.html
Prof. Alan Macdonald
- Animov Y. Differential Geometry and Topology of Curves
- Csikós B. Differential Geometry (FREE!)
- do Carmo M.P. Differential Geometry of Curves and Surfaces – Quite popular for introductory level. Beware that ^ means cross product, and<a,> means a dot b or inner product in this text. Check out the errata list by Bjorn Poonen.
- Hicks N.J. Notes on Differential Geometry [.pdf] (FREE!)
- Kreyszig E. Differential Geometry – Neither do Carmo nor O’Neill introduce the matrix notation when they first discuss the Frenet formulae, Kreyszig does that, which is nice.
- Millman R.S. and Parker G.D. Elements of Differential Geometry
- O’Neill B. Elementary Differential Geometry
- Pressley A. Elementary Differential Geometry – Solution at the back.
- Sharipov R. Course of Differential Geometry (FREE!)
- Struik D.J. Lectures on Classical Differential Geometry
- Zaitsev D. Differential Geometry: Lecture Notes [.pdf] (FREE!)
Tensor Analysis and Manifolds:
- Abraham R., Marsden J.E. and Ratiu T. Manifolds, Tensors, Analysis and Applications (FREE!)
- Bishop R.L. and Goldberg S.I. Tensor Analysis on Manifolds
- Lebedev L.P. and Cloud M.J. Tensor Analysis
- Munkres J.R. Analysis on Manifolds
- Sharipov R. Quick Introduction to Tensor Analysis (FREE!)
- Spivak M. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus – Not as excellent as his books on single variable calculus and the five volumes differential geometry, still better than many authors.
- Arapura D. Introduction to Differential Forms [.pdf] (FREE!)
- Bachman D. A Geometric Approach to Differential Forms
- Cartan H. Differential Forms – Member of Bourbaki, get a taste of the so called French style.
- Darling R.W.R. Differential Forms and Connections
- do Carmo M.P. Differential Forms and Applications
- Flanders H. Differential Forms with Applications to the Physical Sciences
- Morita S. Geometry of Differential Forms
- An Introduction to Differential Geometry T J Willmore
- A comprehensive introduction to differential geometry Michael Spivak
- Applied Differential Geometry a Modern Introduction Tijana T Ivancevic
- A Course in Differential Geometry Thierry Aubin
- Differential Geometry and Statistics MK Murray
- A course in differential geometry and Lie groups S Kumaresan
- Applicable Differential Geometry M Crampin
- Differential Geometry Robert Geroch
- Elementary Differential Geometry AN Pressley
- Topics in Differential Geometry Peter W Michor
- Fundamentals of Differential Geometry Serge Lang
- Methods of Differential Geometry in Analytical Mechanics M de León
- Differential Geometry and Its Applications John Oprea
- Functional Differential Geometry Gerald Jay Sussman
- Applied Differential Geometry William L Burke
- Affine Differential Geometry Katsumi Nomizu
- Geometry of Differential Forms Shigeyuki Morita
- Differential and Riemannian Geometry Detlef Laugwitz
- Manifolds and Differential Geometry Jeffrey Marc Lee
- PDF Differential Geometry Gauge Theories and Gravity M Göckeler
Differential Forms with Applications to the Physical Sciences (Dover Books on Mathematics) Paperback – December 1, 1989 by