Homework set 9 - due 04 / 13 / 2015
نویسنده
چکیده
• Connections in Rn . We have by now defined a number of different notions of differentiation: the differential of maps between manifolds, the exterior derivative of differential forms, and the Lie derivative. To begin to see the need for a new notion of differentiation (which will turn out to be the most fundamental and will apply to general tensor fields) consider first the problem of defining the directional derivative of a vector field X in V =Rn . Let v ∈ TpV . Observe that the obvious definition Dv X = lim t→0 X (p + t v)−X (p) t
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