  A statistical theory of cholesteric liquid crystals composed of short rigid
biaxial molecules is presented. It is derived in the thermodynamic limit at a
small density and a small twist. The uniaxial (biaxial) cholesteric phase is
regarded as a distorted form of the uniaxial (biaxial) nematic phase. The
chirality of the interactions and the implementation of the inversion to the
rotation matrix elements are discussed in detail. General microscopic
expressions for the elastic constants are derived. The expressions involve the
one-particle distribution function and the potential energy of two-body
short-range interactions. It is shown that the elastic constants determine the
twist of the phase. The stability condition for the cholesteric and nematic
phases is presented. The theory is used to study unary and binary systems. The
temperature and concentration dependence of the order parameters, the elastic
constants and the twist of the phase are obtained. The possibility of phase
separation is not investigated.
