In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In fact, this is essentially the basis of frame fields (usually called veirbeins or tetrads in GR contexts), which you seem to allude to with some of your notation.Įdit: As a general comment I should also say that really the Lagrangian formulation of dynamics is the best way to approach the question "what are the equations of motion. In mathematics, conformal geometry is the study of the set of angle-preserving transformations on a space. This can also be seen as equivalent to the statement that there always exist coordinates such that the metric is flat (diagonal with appropriate signature) at a given point (but such a choice cannot always be made globally). u ) is just usual derivative in Euclidean space since for canonical. In a follow up to this question, we can prove that there are two components to acceleration in Newton's Second Law of Motion thusly, 1 Calculate the Christoffel symbols of the canonical flat connection in E3 in. In a flat space, and only in a rectangular coordinate system is each coordinate independent of the other three.
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