  Stellar insolation has been used as the main constraint on a planet's
habitability. However, as more Earth-like planets are discovered around
low-mass stars (LMSs), a re-examination of the role of tides on the
habitability of exoplanets has begun. Those studies have yet to consider the
misalignment between a planet's rotational axis and the orbital plane normal,
i.e. the planetary obliquity. We apply two equilibrium tide theories to compute
the obliquity evolution of terrestrial planets orbiting in the habitable zones
around LMSs. The time for the obliquity to decrease from an Earth-like
obliquity of 23.5 deg to 5 deg, the 'tilt erosion time', is compared to the
traditional insolation habitable zone (IHZ) as a function of semi-major axis,
eccentricity, and stellar mass. We also compute tidal heating and equilibrium
rotation caused by obliquity tides. The Super-Earth Gl581d and the planet
candidate Gl581g are studied as examples for tidal processes. Earth-like
obliquities of terrestrial planets in the IHZ around <0.25 solar mass (M_sun)
stars are eroded in <0.1 Gyr. Only terrestrial planets orbiting stars with
masses >0.9 M_sun experience tilt erosion times larger than 1 Gyr throughout
the IHZ. Terrestrial planets in the IHZ of stars with masses <0.25 M_sun
undergo significant tidal heating due to obliquity tides. The predictions of
the two tidal models diverge significantly for e>0.3. In our two-body
simulations, Gl581d's obliquity is eroded to 0 and its rotation period reached
its equilibrium state of half its orbital period in <0.1 Gyr. Tidal surface
heating on the putative Gl581g is <150 mW/m^2 as long as its eccentricity is
<0.3. Obliquity tides modify the concept of the habitable zone. Tilt erosion of
terrestrial planets orbiting LMSs should be included by atmospheric modelers.
Tidal heating needs to be considered by geologists.
