Homogeneous Hermitian Spaces and Subtwistor Structures
94(47):514.763
Abstract
This paper presents the main results that allow obtaining Hermitian and Kahler homogeneous spaces using subtwistor structures. A subtwistor structure is related to degenerate skew-symmetric 2-form and Riemannian metrics on a manifold. Such a structure is a generalized classic construction of a twistor structure, a symplectic structure, and a Kahler structure for manifolds of arbitrary dimensions with a degenerate skew-symmetric 2-form. It is proved that a subtwistor structure with a vanishing torsion tensor on a Lie group produces the invariant Hermitian structure or Kahler structure on homogeneous space, which is generated by this subtwistor structure. There is a description of an important construction that allows obtaining an invariant Hermitian structure on a homogeneous space of a Lie group of arbitrary dimensions from a left-invariant skew-symmetric degenerate 2-form being a radical that is ideal in a Lie algebra. The mentioned homogeneous space is obtained as a quotient of this Lie group over the radical subgroup.
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Copyright (c) 2026 Евгений Сергеевич Корнев
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