Proving Non-Absorbable Constant with Δξgμν

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Well I have the metric of a sphere given as:
ds2= α (dθ2+ sin2θ dφ2 )

And I'm asked to prove that the constant α is non-absorbable by proving there is no solution to this set of equations:
Δξgμν = ∂gμν/∂α

where:
Δξgμν = gμν;λ ξλ + gλν ξλ;μ + gμλ ξλ;ν


Finally, I'm asked to provide a second way to prove that α is non-absorbable.



I don't understand what it means by non-absorbable at all. Do you know where am I supposed to find what it is? From books I have Weinberg's "Gravitation and Cosmology Principles and appls of GTR". In addition, any hint would be appreciated...
Thank you..
 
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This is my 1st try to solve it, the equations I ended up are the 5 bellow, which cannot be solved (i guess). The last one reads ξ2,2=1/2α..

I also got a problem with 0=1...

What do you think?
 

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