Could you give a recommendation for differential geometry or curves and surfaces with lots of examples and calculations?
I need lots of examples to understand a topic therefore it would great if there are some book with good calculations.
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Differential Geometry and its Applications, by John Oprea is my favorite book on curves and surfaces, I have learned an absurd deal from it. If you're feeling more daring and wants to see how the theory can be done simultaneously in $\Bbb R^3$ and Minkowski space, I have a book myself about it. – Ivo Terek Feb 09 '21 at 22:16
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Barrett O'Neill's Elementary Differential Geometry. A classic, you can't go wrong with this one..
MathematicianByMistake
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The ones I used and liked were:
Differential Geometry of Curves and Surfaces - Manfredo Do Carmo
Modern Differential Geometry of Curves and Surfaces with Mathematica - Alfred Gray
Tiago Abreu
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The second one (Gray) has more examples and calculations, I recommend checking out both of them. Also, Wolfram Mathematica is a very nice tool for calculations and creating nice and visual examples :) – Tiago Abreu Feb 09 '21 at 21:52
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For the geometry of surfaces I recommend the book Differential Geometry of Curves and Surfaces by Manfredo Do Carmo, which is clear, self-contained and with a lot of examples and exercises.
If you want to go further and learn modern differential geometry (manifolds etc) an excellent book is An introduction to manifolds by Loring Tu, which contains a lot of examples and explicit calculations. Moreover it is self-contained, and has a lot of appendices in the case you have to strengthen you background.
Another very good book about manifolds is Introduction to smooth manifolds by Lee. You can read some of its chapters as a complement of Tu’s book, indeed it contains some important topics that you can’t find in the book of Loring Tu.
Tommaso Rossi
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