Subject: question about the tangent bundle
Date: Fri, 18 Oct 2002 15:11:26 -0400 (EDT)
From: keramat ali <keramat_ali2002@yahoo.ca>
To: dmd1@lehigh.edu

Dear Topologists,

I am learning differential geometry by myself and the
following question seems to be not addressed by the
many textbooks that I came across.

According to the textbooks, it seems necessary to go
to the tangent bundle in order to study the base
manifold. For me the tangent bundle seems to be more
difficult to imagine. But the textbooks also say that
"because the frame bundle has n+nxn linearly
independent vector fields on it, where n=dimM, it is
more simple."  To anyone who can help me understand
the philosophy here,
I would sincerely appreciate. To push the question a
little bit further, if it makes sense to consider the
tangent bundle, why should we stop there while not
considering the tangent bundle of the tangent bundle
and so fourth?

Sincerely,

K.Ali

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