  With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method
in the three-dimensional coordinate-mesh representation, we have carried out a
systematic theoretical search for the superdeformed and hyperdeformed
rotational bands in the mass A=30-50 region. Along the N=Z line, we have found
superdeformed solutions in 32S, 36Ar, 40Ca, 44Ti, and hyperdeformed solutions
in 36Ar, 40Ca, 44Ti, 48Cr. The superdeformed band in 40Ca is found to be
extremely soft against both the axially symmteric (Y30) and asymmetric (Y31)
octupole deformations. An interesting role of symmetry breaking in the mean
field is pointed out.
