  The form of Hamiltonian and Diffeomorphism constraints in
Sen-Ashtekar-Barbero-Immirzi variables is well known for the spacelike 3+1 ADM
foliation. It is also known that Sen-Ashtekar-Barbero-Immirzi connection can be
introduced only in 3 dimensional space and does not work for $D > 3$. The
reason it works in $D = 3$ is due to existence of isomorphism between $so(3)$
algebra and $R^3$ space with vector product. It turns out that similar
isomorphism exists between $so(2,1)$ algebra and $R^3_{2,1}$ space algebra with
respect to its vector product. By using this isomorphism we find both analog of
Sen-Ashtekar-Barbero-Immirzi connection for timelike 3+1 foliation and
corresponding forms of Gauss, Diffeomorphism and Hamiltonian constraints. We
then combine spacelike and timelike foliation constraints into the generalized
form of the Hamiltonian and Diffeomorphism constrains using generalized
Sen-Ashtekar-Barbero-Immirzi connection variables. We prove that Immirzi
parameter is covariant with respect to timelike-spacelike ADM foliation change
as in both cases in self-dual Ashtekar case it disappears in Hamiltionian
constraint keeping it polynomial.
