  Let $\mathbf{g}$ be a pseudo--Riemanian metric of arbitrary signature on a
manifold $\mathbf{V}$ with conventional $n+n$ dimensional splitting, $\ n\geq
2,$ determined by a nonholonomic (non--integrable) distribution $\mathcal{N}$
defining a generalized (nonlinear) connection and associated nonholonomic frame
structures. We shall work with a correspondingly adapted linear metric
compatible connection $\hat{\mathbf{D}}$ and its nonzero torsion
$\hat{\mathcal{T}}$, both completely determined by $\mathbf{g}$. Our first goal
is to prove that there are certain generalized frame and/or jet transforms and
prolongations with $(\mathbf{g},\mathbf{V})\rightarrow
(\hat{\mathbf{g}},\hat{\mathbf{V}})$ into explicit classes of solutions of some
generalized Einstein equations $\hat{\mathbf{R}}\mathit{ic}=\Lambda
\hat{\mathbf{g}}$, $\Lambda =const$, encoding various types of nonholonomic)
Ricci soliton configurations and/or jet variables and symmetries. The second
goal is to solve additional constraint equations for zero torsion,
$\hat{\mathcal{T}}=0$, on generalized solutions constructed in explicit forms
with jet variables and extract Levi-Civita configurations. This allows us to
find generic off-diagonal exact solutions depending on all space time
coordinates on $\mathbf{V}$ via generating and integration functions and
various classes of constant jet parameters and associated symmetries. We shall
study (third goal) how such generalized metrics and connections can be related
by so-called "half-conformal" and/ or jet deformations of certain sub-classes
of solutions with one, or two, Killing symmetries. Finally, there are
considered some examples when exact solutions are constructed as nonholonomic
jet prolongations of the Kerr metrics, with possible Ricci soliton
deformations, and characterized by nonholonomic jet structures and generalized
connections.
