  The search for transiting habitable exoplanets has broadened to include
several types of stars that are smaller than the Sun in an attempt to increase
the observed transit depth and hence the atmospheric signal of the planet. Of
all spectral types, white dwarfs are the most favorable for this type of
investigation. The fraction of white dwarfs that possess close-in rocky planets
is unknown, but several large angle stellar surveys have the photometric
precision and cadence to discover at least one if they are common. Ultraviolet
observations of white dwarfs may allow for detection of molecular oxygen or
ozone in the atmosphere of a terrestrial planet. We use archival Hubble Space
Telescope data from the Cosmic Origins Spectrograph to search for transiting
rocky planets around UV-bright white dwarfs. In the process, we discovered
unusual variability in the pulsating white dwarf GD 133, which shows slow
sinusoidal variations in the UV. While we detect no planets around our small
sample of targets, we do place stringent limits on the possibility of
transiting planets, down to sub-lunar radii. We also point out that
non-transiting small planets in thermal equilibrium are detectable around
hotter white dwarfs through infrared excesses, and identify two candidates.
