  The generalised Raychaudhuri equations derived by Capovilla and Guven are
exclusively for extremal, timelike Nambu--Goto membranes. In this article, we
construct the corresponding equations for string world--sheets in the presence
of a background Kalb--Ramond field. We analyse the full set of equations by
concentrating on special cases in which the generalised shear or the
generalised rotation or both are set to zero. If only the generalised shear is
set to zero then it is possible to identify the components of the generalised
rotation with the projections of the field strength of the Kalb--Ramond
potential.
