2023/11/05 by Viktor Abramov, Abramov, Viktor, Olga Liivapuu +1
Chemistry · Physics and Astronomy · #17A40 #20N10 #53C07 #Advanced Mathematical Theories and Applications #Advanced NMR Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2311.02606
openalex publication_date 2023/11/05 · openalex created_date 2023/11/08 · openalex updated_date 2026/07/28
We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional subspaces and in each subspace there is an irreducible representation of the rotation group SO(3) -> SO(5). We find two independent SO(3)-invariants of ternary skew-symmetric tensors, where one of them is the Hermitian metric and the other is the quadratic form. We find the stabilizer of this quadratic form and its invariant properties. Making use of these invariant properties we define a SO(3)-irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with a SO(3)-irreducible geometric structure, find its curvature and torsion. The structures proposed in this paper and their study are motivated by a ternary generalization of the Pauli's principle proposed by R. Kerner.