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Tedjn
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A little embarrassing, but I have had very little exposure to anything involving manifolds and am trying to work through these notes over spring break. I will have many questions on even the simplest concepts. In this thread I hope to outline these as I encounter them, and if anyone can help I would be very grateful.
Even in the beginning of the preliminary, I am encountering some difficulties. In the definition of coordinate frame associated with a chart x, the notes say it is a tuple of vector fields. What are these vector fields given by the partial derivative notation as applied to a general differentiable manifold? How many are there, n of them? Is each defined over U, the domain of x? And of course, is there some better intuitive way to understand this frame concept that I haven't seen?
These are some questions to start off just in the first paragraph, so you see what level I am at. Thanks in advance for any insights :)
Even in the beginning of the preliminary, I am encountering some difficulties. In the definition of coordinate frame associated with a chart x, the notes say it is a tuple of vector fields. What are these vector fields given by the partial derivative notation as applied to a general differentiable manifold? How many are there, n of them? Is each defined over U, the domain of x? And of course, is there some better intuitive way to understand this frame concept that I haven't seen?
These are some questions to start off just in the first paragraph, so you see what level I am at. Thanks in advance for any insights :)