- #1
kiuhnm
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I'm reading "The Geometry of Physics" by Frankel. Exercise 1.3(1) asks what would be wrong in defining ##||X||## in an ##M^n## by
$$||X||^2 = \sum_j (X_U^j)^2$$ The only problem I can see is that that definition is not independent of the chosen coordinate systems and thus not intrinsic to ##M^n##. Is there anything else I'm missing?
BTW, I'm not sure this is Differential Geometry... Is this Topology?
$$||X||^2 = \sum_j (X_U^j)^2$$ The only problem I can see is that that definition is not independent of the chosen coordinate systems and thus not intrinsic to ##M^n##. Is there anything else I'm missing?
BTW, I'm not sure this is Differential Geometry... Is this Topology?