2-dimensional differentiable surfaces

[Dragonfall]

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

I need to know about geodesics, etc.

 

[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.

 

[micromass]

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.

 

[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.

 

[blue_raver22]

I can provide some information on 2-dimensional differentiable surfaces. These surfaces are mathematical structures that can be described by two parameters, such as longitude and latitude on a globe. They are smooth and continuous, meaning that they have no sharp edges or corners.

To learn more about 2-dimensional surfaces, I would recommend the book "Differential Geometry of Curves and Surfaces" by Manfredo do Carmo. This book covers the fundamentals of 2-dimensional surfaces, including geodesics, curvature, and the Gauss-Bonnet theorem. It also includes examples and exercises to help deepen your understanding of these concepts.

If you specifically want to learn about 3-spheres, I would suggest "Introduction to Topological Manifolds" by John Lee. This book covers the basics of 3-dimensional manifolds, including 3-spheres, and also includes a chapter on geodesics and curvature.

I hope these recommendations help in your understanding of 2-dimensional surfaces and geodesics. Happy exploring!