Curvature tensors and Singer invariants of four-dimensional homogeneous spaces
We show that the Singer invariant of a four-dimensional homogeneous space is at most .
We show that the Singer invariant of a four-dimensional homogeneous space is at most .
A six-parameter family is constructed of (algebraic) Riemannian curvature tensors in dimension four which do not belong to any curvature homogeneous space. Also a general method is given for a possible extension of this result.