SO(3)-Irreducible Geometry in Advanced Dimension 5 and Ternary Generalization of Pauli Exclusion Precept
Authors: Viktor Abramov, Olga Liivapuu
Summary: We suggest a notion of a ternary skew-symmetric covariant tensor of third order, think about it as a three-dimensional matrix and research a ten-dimensional complicated area of those tensors. We break up this area right into a direct sum of two five-dimensional subspaces and in every subspace there may be an irreducible illustration of the rotation group SO(3) -> SO(5). We discover two unbiased SO(3)-invariants of ternary skew-symmetric tensors, the place certainly one of them is the Hermitian metric and the opposite is the quadratic type. We discover the stabilizer of this quadratic type and its invariant properties. Making use of those invariant properties we outline a SO(3)-irreducible geometric construction on a five-dimensional complicated Hermitian manifold. We research a connection on a five-dimensional complicated Hermitian manifold with a SO(3)-irreducible geometric construction, discover its curvature and torsion. The constructions proposed on this paper and their research are motivated by a ternary generalization of the Pauli’s precept proposed by R. Kerner.
