  We study geometric properties of a random Gaussian short-time correlated
velocity field by considering statistics of a passively advected metric tensor.
That describes universal properties of fluctuations of tensor objects frozen
into the fluid and passively advected by it. The problem of one-point
statistics of co- and contravariant tensors is solved exactly, provided the
advected fields do not reach dissipative scales, which would break the symmetry
of the problem. Asymptotic in time duality of the problem is established, which
in the three-dimensional case relates the probabilities of the volume
deformations into "tubes" and into "sheets".
