  We discuss the first moments of the parity-even Generalized Parton
Distributions (GPDs) in a nucleon, corresponding to six (generalized) vector
form factors. We evaluate these fundamental properties of baryon structure at
low energies, utilizing the methods of covariant Chiral Perturbation Theory in
the baryon sector (BChPT). Our analysis is performed at leading-one-loop order
in BChPT, predicting both the momentum and the quark-mass dependence for the
three (generalized) isovector and (generalized) isoscalar form factors, which
are currently under investigation in lattice QCD analyses of baryon structure.
We also study the limit of vanishing four-momentum transfer where the
GPD-moments reduce to the well known moments of Parton Distribution Functions
(PDFs). For the isovector moment <x>_{u-d} our BChPT calculation predicts a new
mechanism for chiral curvature, connecting the high values for this moment
typically found in lattice QCD studies for large quark masses with the smaller
value known from phenomenology. Likewise, we analyze the quark-mass dependence
of the isoscalar moments in the forward limit and extract the contribution of
quarks to the total spin of the nucleon. We close with a first glance at the
momentum dependence of the isoscalar C-form factor of the nucleon.
