Calculus Tangent & Cotangent Bundles in Principal Bundles

[Feynman]

Hello,
I've 2 qustions :
1.Calculus the tangent bundel TM and the cotangent bundles T*M like a bundles associates to the principal bundle B(M) of the reper of TM


2.If M has a riemannian structure set up the principale bundels B'(M) of orthonormal system of TM in case of M=S^2 , we can identify B'(M) to O^3

 

[quantumdude]

1. I see no questions in your post.

2. What is a "reper"?

Please try to elaborate, and don't forget to show how you started the problems yourself.

 

[Feynman]

describe the tangent bundel TM and the cotangent bundles T*M as a associated bundles to the principal bundel B(M) the system of TM
2.If M has a riemannian structure set up the principale bundels B'(M) of orthonormal system of TM in case of M=S^2 , we can identify B'(M) to the Lie group O^3