Abstract:
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).
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