A characterization of the line set of an odd-dimensional Baer subspace

Generalizing a theorem of Beutelspacher and Seeger, we consider line sets inP=PG(2t + 1,q),t IN, with the following properties: (1) any (t + 1)-dimensional subspace ofP contains at least one line of , (2) if a pointx ofP is incident with at least two lines of then the points in the factor geometryP/x which are induced by the lines of throughx form a blocking set of type (t, 1) inP/x, (3) any line of is coplanar with at least one further line of . We will show that the examples of minimal cardinality are exactly the line sets of Baer subspaces ofP.