Analog of a Compact Calabi-Yau Manifold based on the Algebra of Signatures
Abstract
Mikhail Batanov-Gaukhman
A multidimensional Ricci-flat space is proposed, in which additional dimensions harmoniously compensate each other’s manifestations in accordance with the internal topological structure of a given manifold, i.e., without additional conditions. At the same time, the geometric and topological parameters of such a space, developed within the framework of Algebra the Signature, turned out to be sufficient for the creation of metric-dynamic models of all elementary particles included in the Standard Model [1-10]. In particular, it is possible to geometrize such concepts as charge, spin, inertial mass, colors and confinement of the quarks, and also propose ways of metric-dynamically substantiating the nature of gravity, dark matter and energy, etc. In connection with these possibilities of the multidimensional geometry based on the Algebra of signature, the multidimensional Ricci-flat space generated by it can be proposed as an alternative to the Calabi-Yau manifold used in superstring theory.
