On a hypersurface in the space of applied covectors

The present paper continues a series of the author's publications devoted to immersions of various manifolds into point-vector spaces (see examples in the list of references [2,3,7]). A six- dimensional point-vector space D6 is constructed for the original three-dimensional affine space. A point of the space is an applied covector and a vector is an ordered couple composed of a vector and a covector. A hypersurface of the obtained space contains pseudo-Riemannian metrics induced by the intrinsic metrics of space D6. A connection of the hypersurface called natural has been built, as well as the Levi–Civita connection. Geodesic lines of both connections are examined (for the first one, up to the full characterization).