2-dimensional differentiable surfaces

  • Context: Graduate 
  • Thread starter Thread starter Dragonfall
  • Start date Start date
  • Tags Tags
    Differentiable Surfaces
Click For Summary

Discussion Overview

The discussion revolves around recommendations for books on 2-dimensional surfaces, specifically focusing on topics such as geodesics and the nature of 3-spheres. The context includes references to differential geometry and its applications.

Discussion Character

  • Technical explanation, Meta-discussion

Main Points Raised

  • One participant seeks recommendations for books on 2-dimensional surfaces, mentioning a need to understand geodesics.
  • Another participant suggests "Differential Geometry of Curves and Surfaces" by Do Carmo as a suitable resource.
  • A later reply clarifies that 3-spheres are 3-manifolds, not 2-surfaces embedded in ##\mathbb{R}^{3}##.
  • Additional recommendations include books by Millman and Parker, O'Neill, and Lee, with a note that Lee's book may not be suitable for immediate study.
  • One participant expresses gratitude and mentions a prior course in differential geometry, indicating familiarity with Do Carmo's work.

Areas of Agreement / Disagreement

Participants generally agree on the recommendation of Do Carmo's book, but there is a clarification regarding the classification of 3-spheres, indicating a nuanced understanding of the topic. No consensus on a single best resource exists, as multiple books are suggested.

Contextual Notes

There is an implicit assumption that readers have some background in differential geometry, as one participant references a previous course and existing materials.

Dragonfall
Messages
1,023
Reaction score
5
What is a good book on 2-dimensional surfaces (3-spheres, etc.)?

I need to know about geodesics, etc.
 
Physics news on Phys.org
Differential Geometry of Curves and Surfaces - Do Carmo.

EDIT: By the way, 3-spheres aren't 2-surfaces embedded in ##\mathbb{R}^{3}##. As you could guess from the name, they are 3-manifolds.
 
Last edited:
WannabeNewton said:
Differential Geometry of Curves and Surfaces - Do Carmo.

This is the classic on curves and surfaces! So I second it.

Other nice books are Millman and Parker: https://www.amazon.com/dp/0132641437/?tag=pfamazon01-20
and Oneill: https://www.amazon.com/dp/0120887355/?tag=pfamazon01-20

And then there is of course Lee: https://www.amazon.com/dp/1441999817/?tag=pfamazon01-20 But this is not a book you want to read now, start with more "classical differential geometry" first. If you're interested, then you should read this book eventually though.
 
OK thanks a bunch! I took a course on differential geometry years ago and actually still have my copy of Do Carmo and I need to get re-acquainted with it for thesis reasons.
 

Similar threads

Graduate Geodesics on three dimensional graph
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad How can a sphere be transformed using differential geometry?
  • · Replies 17 ·
Replies
17
Views
4K
Graduate Differential movement along a curved surface
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Parallel Transport Along Geodesic
  • · Replies 6 ·
Replies
6
Views
5K
High School Oriented Surfaces & Surface Area: Investigating the Impact
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Assumptions about the convex hull of a closed path in a 4D space
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Flat surface to curved surface
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Round 3-sphere symmetries as subspace of 4D Euclidean space
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Definition of inertia tensor from a differential geometry viewpoint
  • · Replies 15 ·
Replies
15
Views
3K
Graduate How to understand when surface terms go to zero
  • · Replies 6 ·
Replies
6
Views
2K