  We study the phase diagram of two-dimensional Bose-Fermi mixtures of
ultracold atoms on a triangular optical lattice, in the limit when the velocity
of bosonic condensate fluctuations is much larger than the Fermi velocity.
  We contrast this work with our previous results for a square lattice system
in Phys. Rev. Lett. {\bf 97}, 030601 (2006).
  Using functional renormalization group techniques we show that the phase
diagrams for a triangular lattice contain exotic superconducting phases. For
spin-1/2 fermions on an isotropic lattice we find a competition of $s$-, $p$-,
extended $d$-, and $f$-wave symmetry, as well as antiferromagnetic order. For
an anisotropic lattice, we further find an extended p-wave phase. A Bose-Fermi
mixture with spinless fermions on an isotropic lattice shows a competition
between $p$- and $f$-wave symmetry.
  These phases can be traced back to the geometric shapes of the Fermi surfaces
in various regimes, as well as the intrinsic frustration of a triangular
lattice.
