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

WWGD

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 thoery 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.

shoehorn

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.

lavinia

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.

lavinia

I also remember that Thorne and Wheeler have an elementary book on GR called Black Holes. I think they work in concrete examples.