Hypersurface homogeneous locally rotationally symmetric spacetimes admitting conformal symmetries

All hypersurface homogeneous locally rotationally symmetric spacetimes which admit conformal symmetries are determined and the symmetry vectors are given explicitly. It is shown that these spacetimes must be considered in two sets. One set containing Ellis Class II and the other containing Ellis Class I, III LRS spacetimes. The determination of the conformal algebra in the first set is achieved by systematizing and completing results on the determination of CKVs in 2+2 decomposable spacetimes. In the second set new methods are developed. The results are applied to obtain the classification of the conformal algebra of all static LRS spacetimes in terms of geometrical variables. Furthermore all perfect fluid nontilted LRS spacetimes which admit proper conformal symmetries are determined and the physical properties some of them are discussed.