If ##\sigma## is an affine paramter, then the only freedom of choice we have to specify another affine parameter is ##a\sigma+b##, a,b constants. [1]
For the tangent vector, ##\xi^{a}=dx^{a}/du##, along some curve parameterized by ##u##
My book says that ' if ##\xi^{a}\xi_{a}\neq 0##, then by...