  Nodal noncentrosymmetric superconductors have topologically nontrivial
properties manifested by protected zero-energy surface states. Specifically, it
was recently found that zero-energy surface flat bands of topological origin
appear at their surface. We show that the presence of certain inversion-type
lattice symmetries can give rise to additional topological features of the gap
nodes, resulting in surface states forming one-dimensional arcs connecting the
projections of two nodal rings. In addition, we demonstrate that Majorana
surface states can appear at time-reversal-invariant momenta of the surface
Brillouin zone, even when the system is not fully gapped in the bulk. Within a
continuum theory we derive the topological invariants that protect these
different types of zero-energy surface states. We independently derive general
conditions for the existence of zero-energy surface bound states using the
complementary quasiclassical scattering theory, explicitly taking into account
the effects of spin-orbit splitting of the bands. We compute surface
bound-state spectra for various crystal point-group symmetries and
orbital-angular-momentum pairing states. Finally, we examine the signatures of
the arc surface states and of the zero-energy surface flat bands in
tunneling-conductance spectra and discuss how topological phase transitions in
noncentrosymmetric superconductors could be observed in experiments.
