The Schouten-van Kampen affine connection adapted to an almost (para) contact metric structure

We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.Comment: Presented at XVII Geometrical Seminar, Zlatibor 2012, Serbi

A note on almost kähler manifolds

For anyn ≥ 2, we give examples of almost Kähler conformally flat manifoldsM 2n which are not Kähler. We discuss the meaning of these examples in the context of the Goldberg conjecture on almost Kahler manifold

Computer-aided design of industrial installations

The paper concerns the design of industrial installations using computer programs. It also contains a description of problems that must be solved by a constructor who designs industrial installations, their components and characteristics at different stages of industrial design

On compact holomorphically pseudosymmetric K\"ahlerian manifolds

For compact K\"ahlerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric K\"ahlerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem. Recently, the first examples of compact, simply connected essentially holomorphically pseudosymmetric K\"ahlerian manifolds are discovered by W. Jelonek. In his examples, the structure functions change their signs on the manifold

On pseudo-Riemannian manifolds with recurrent concircular curvature tensor

It is proved that every concircularly recurrent manifold must be necessarily a recurrent manifold.Comment: 5 page