We analyse the influence of rotation on shapes of pulse profiles of
fast-rotating (millisecond) pulsars. Corotation has two opposing effects: 1)
the caustic enhancement of the trailing side (TS) by aberration and retardation
(AR), which squeezes the emission into a narrower phase interval; 2) the
weakening of the TS caused by the asymmetry of curvature radiation about the
dipole axis. Analysis of the radii of curvature of electron trajectories in the
inertial observer's frame (IOF) enables these two effects to be considered
together. We demonstrate that for dipolar magnetic field lines on the TS there
exists a `caustic phase' beyond which no emission can be observed. This phase
corresponds to the zero (or minimum) curvature of the IOF trajectories and
maximum bunching of the emission. The maximum gradient of polarisation angle
(PA) in the S-shaped PA curve is also associated with the curvature minimum and
occurs at exactly the same phase. The asymmetry of trajectory curvature with
respect to the dipole axis affects the curvature emissivity and the efficiency
of pair production, suggesting a minimum at the caustic phase. Emission over a
fixed range of altitudes, as expected in millisecond pulsars, leads to broad
leading profiles and sharp peaks with a cutoff phase on the TS. We apply our
results to the main pulse of the 5 ms pulsar J1012+5307.Comment: 12 pages, 7 figures, submitted to MNRA