  It is formulated a new 'anholonomic frame' method of constructing exact
solutions of Einstein equations with off--diagonal metrics in 4D and 5D
gravity. The previous approaches and results are summarized and generalized as
three theorems which state the conditions when two types of ansatz result in
integrable gravitational field equations. There are constructed and analyzed
different classes of anisotropic and/or warped vacuum 5D and 4D metrics
describing ellipsoidal black holes with static anisotropic horizons and
possible anisotropic gravitational polarizations and/or running constants. We
conclude that warped metrics can be defined in 5D vacuum gravity without
postulating any brane configurations with specific energy momentum tensors.
Finally, the 5D and 4D anisotropic Einstein spaces with cosmological constant
are investigated.
