  The new principle of constrained twistor-like variables is proposed for
construction of the Cartan 1-forms on the worldsheet of the D=3,4,6 bosonic
strings. The corresponding equations of motion are derived. Among them there
are two well-known Liouville equations for real and complex worldsheet
functions W(s,\bar s). The third one in which W(s,\bar s) is replaced by the
quaternionic worldsheet function is unknown and can be thought of as that of
the SU(2) nonlinear sigma-model governing the classical dynamics of the bosonic
string in D=6.
