  We present a model of the electronic properties of monolayer transition-metal
dichalcogenides based on a tight binding approach which includes the effects of
strain and curvature of the crystal lattice. Mechanical deformations of the
lattice offer a powerful route for tuning the electronic structure of the
transition-metal dichalcogenides, as changes to bond lengths lead directly to
corrections in the electronic Hamiltonian while curvature of the crystal
lattice mixes the orbital structure of the electronic Bloch bands. We first
present an effective low energy Hamiltonian describing the electronic
properties near the K point in the Brillouin zone, then present the corrections
to this Hamiltonian due to arbitrary mechanical deformations and curvature in a
way which treats both effects on an equal footing. This analysis finds that
local area variations of the lattice allow for tuning of the band gap and
effective masses, while the application of uniaxial strain decreases the
magnitude of the direct band gap at the K point. Additionally, strain induced
bond length modifications create a fictitious gauge field with a coupling
strength that is smaller than that seen in related materials like graphene. We
also find that curvature of the lattice leads to the appearance of both an
effective in-plane magnetic field which couples to spin degrees of freedom and
a Rashba-like spin-orbit coupling due to broken mirror inversion symmetry.
