Request: Solved Problems in R.Geometry; Connections, etc.

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In summary, the individual is seeking resources for solved problems and examples in the areas of connections, covariant differentiation, and Riemannian geometry to assist in a presentation to non-mathematicians. Suggestions include the Problem Book in Relativity and Gravitation by Lightman et al, any standard text on general relativity, and books on differential geometry and general relativity by Struck and Thorne and Wheeler. The use of examples, such as differentiating vector fields in Euclidean space and projecting onto a surface's tangent space, is also recommended.
  • #1
WWGD
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Hi, everyone:

I need to give a small presentation in front of a group of non-mathematicians
on connections, and covariant differentiation; I can handle the theory O.K-enough
but I would like to have some solved problems/examples. Anyone know of a book
or other sources with solved problems/examples on connections, riemannian geometry,
say, books for physicists, etc.

Thanks in Advance.
 
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  • #2
My copy seems not to be on my shelf at the moment, but I recall that Problem Book in Relativity and Gravitation by Lightman et al has plenty of solved problems in this area. Any standard text on general relativity should also contain what you're looking for.
 
  • #3
WWGD said:
Hi, everyone:

I need to give a small presentation in front of a group of non-mathematicians
on connections, and covariant differentiation; I can handle the theory O.K-enough
but I would like to have some solved problems/examples. Anyone know of a book
or other sources with solved problems/examples on connections, riemannian geometry,
say, books for physicists, etc.

Thanks in Advance.

For me the simplest picture comes from differentiating vector fields in Euclidean space.
Next simplest is the projection of the derivative onto a surface's tangent space. So give a vector field along a curve on a surface - differentiate is in some direction on the surface then project.

Work out examples on the sphere, along a curve in Eucliean space, on a helicoid.

You could then use the same examples to easily compute some geodesics.

Books an elementary DG are full of examples e.g. Struck's History of Diff Geo.
 
  • #4
I also remember that Thorne and Wheeler have an elementary book on GR called Black Holes. I think they work in concrete examples.
 
  • #5


Hi there,

It's great that you are preparing a presentation on connections and covariant differentiation for a group of non-mathematicians. I understand the importance of providing concrete examples and applications to help others understand complex concepts.

There are several resources available that provide solved problems and examples on connections and Riemannian geometry. One book that I would recommend is "A Comprehensive Introduction to Differential Geometry" by Michael Spivak. This book covers a wide range of topics including connections, covariant differentiation, and Riemannian geometry, and includes many solved problems and examples throughout the text.

Another helpful resource is the "Lecture Notes on Differential Geometry" by John Lee. This book also has a section on connections and provides numerous solved problems and examples.

Additionally, there are many online resources that offer solved problems and examples, such as math.stackexchange.com and mathoverflow.net. These websites have a community of mathematicians and scientists who are willing to help and provide solutions to specific problems.

I hope these suggestions are helpful in finding the resources you need for your presentation. Good luck!
 

1. What is R.Geometry?

R.Geometry is a programming language commonly used for statistical analysis and data visualization. It is an open-source software that allows for efficient manipulation and analysis of data.

2. What are solved problems in R.Geometry?

Solved problems in R.Geometry are commonly used as examples to demonstrate how the language can be used to solve real-world problems. These problems can range from basic statistical analyses to more complex data modeling tasks.

3. How can I learn about connections in R.Geometry?

To learn about connections in R.Geometry, it is recommended to start with the basic functions and syntax of the language. From there, you can explore more advanced concepts such as data connections, API connections, and database connections.

4. Can R.Geometry be used for geometric calculations?

Yes, R.Geometry has functions and libraries specifically designed for geometric calculations. Some commonly used packages for this purpose include rgeos, sp, and maptools.

5. Are there any resources available for practicing solved problems in R.Geometry?

Yes, there are many online resources available for practicing solved problems in R.Geometry. Some popular websites include DataCamp, Kaggle, and Coursera, which offer interactive courses and challenges to help improve your skills in the language.

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