# 2-dimensional differentiable surfaces

1. Apr 15, 2013

### Dragonfall

What is a good book on 2-dimensional surfaces (3-spheres, etc.)?

I need to know about geodesics, etc.

2. Apr 15, 2013

### WannabeNewton

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: Apr 15, 2013
3. Apr 15, 2013

### micromass

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

Other nice books are Millman and Parker: https://www.amazon.com/Elements-Differential-Geometry-Richard-Millman/dp/0132641437
and Oneill: https://www.amazon.com/Elementary-Differential-Geometry-Revised-Second/dp/0120887355/

And then there is of course Lee: https://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/1441999817 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.

4. Apr 15, 2013

### Dragonfall

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.