Baecklund transformation on surfaces with (k1-m) (k2-m) = -l2

In this paper, we generalize the Baecklund theorem on surfaces with negative Gaussian Curvature K to the surfaces with (k1-m)(k2-m)=l2 where k1 and K2 are principal curvatures, m(>=0) and l(>0) are arbitrary constants. We present a geometrical method to construct a family of surfaces with (k1-m) (k2-m) = -l2 from known surfaces with (k1-m) (k2-m) = -l2. When m=0, this is the Baecklund theorem on surfaces with K=k1k2=-l2. (author). 5 refs