  We discuss some geometrical aspects of the semiclassical quantization of
string solutions in Type IIB Green-Schwarz action on $\ads_5\times \sphere^5$.
We concentrate on quadratic fluctuations around classical configurations,
expressing the relevant differential operators in terms of (intrinsic and
extrinsic) invariants of the background geometry. The aim of our exercises is
to present some compact expressions encoding the spectral properties of bosonic
and fermionic fluctuations. The appearing of non-trivial structures on the
relevant bundles and their role in concrete computations are also considered.
We corroborate the presentation of general formulas by working out explicitly a
couple of relevant examples, namely the spinning string and the latitude BPS
Wilson loop.
