r/math • u/Psychological_Wall_6 • 2d ago

Problem book on the differential geometry of curves and surfaces

Hello! I need some problem books to accompany the book Differential Geometry of Curves and Surfaces by M. Di Carmo. Thank you!

20 Upvotes

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16

u/Bitter-Morning-5833 2d ago

Doesn't the book have a bunch of exercises? It's been years since I read it, but if I remember correctly there's plenty to work through.

10

u/nulvoid000 2d ago

What’s wrong with the exercise already provided there? Also it’s Do Carmo

3

u/Psychological_Wall_6 2d ago

I need more

1

u/Carl_LaFong 2d ago

Why? Are you studying for a test?

4

u/Psychological_Wall_6 2d ago

It's just that our course is technically called "The Computational Geometry of Curves and Surfaces" and every book I find does not have the necessary exercises. And yes, I'm studying for a test

5

u/Carl_LaFong 2d ago

You had homework problems and you’re looking tor similar ones? What textbook is being used for the course?

4

u/ABranchingLine 2d ago

You can apply the theory from that book on most curves. Pick a curve. Calculate the Frenet-Serret frame, find curvature, torsion, etc. Infinite exercises.

1

u/Organic-Product-6613 2d ago

i think most books on curves and surfaces will have a lot of common questions with Docarmo...

1

u/its_t94 Differential Geometry 2d ago

This book is basically a version of do Carmo done in Minkowski 3-space, but does the theory in Euclidean 3-space too, both at the same time

https://www.routledge.com/Introduction-to-Lorentz-Geometry-Curves-and-Surfaces/Couto-Lymberopoulos/p/book/9780367624118

1

u/MeserYouUp 2d ago

The first few chapters of General Relativity in a Nutshell by A. Zee have a lot of good problems on 2 and 3 dimensional surfaces.

1

u/Honest_Archaeopteryx 2d ago

Is there a schaum’s outline for this?

1

u/Turbulent_Baker7758 1d ago

Seeing your responses, I would like to offer "Modern Differential Geometry of Curves and Surfaces with Mathematica" by Gray and maybe a look through O'Neill's "Elementary Differential Geometry"