A New Approach to Differential Geometry using Clifford's Geometric Algebra by John Snygg

Author:John Snygg
Language: eng
Format: epub
Publisher: Birkhäuser Boston, Boston, MA

(6.32)

as before, the direction of the unit vector n(s) is chosen so that t(s), n(s) is “right handed.” If V 1(s), V 2(s) is a pair of orthonormal right handed vectors that are parallel transported along the curve x(s), then we can write

Since ∇  s V 1(s) =  ∇  s V 2(s) = 0, we have

(6.33)

(6.34)

Problem 119.

For theoretical discussions of curves, it is convenient to use an arc length parameter. However in actual practice, solving the equation ds ∕ dt = v(t) and then obtaining the inverse function t(s) can complicate the computations. However, the desired entities can be computed without using an explicit form of t(s). Show

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