Abstract
The local structure of a 3-dimensional essentially weakly para-cosymplectic manifold is described in two ways: using special adapted local frames and special coordinate systems. This enables a description of the curvature of such manifolds. Local isometries and Killing vector fields are also investigated. It is proved that if a 3-dimensional weakly para-cosymplectic manifold is locally homogeneous as a Riemannian manifold, then it is para-cosymplectic or locally flat. Then a classification of such manifolds is given.
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