I know that we can generate an affine connection on a GL(n) bundle.If we have a fibre bundle whose structure group G is the subgroup of GL(n) with diagonalizable matrices M whose eigenvalues are +1 or -1 (and for which there must be at least one eigenvalue of -1) and the Identity I( ie G={M,I:M^2=I} but M is unequal to I), how can I generate a connection 1-form on the G-bundle which is related to the affine connection on GL(n)?
Pls I would also like it localized to show each index.I hope I got the message across. Thanks in Advance.