Left invariant complex structures on U(2) and SU(2) × SU(2) revisited. ∗
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چکیده
Left invariant complex structures on U (2) and SU (2) × SU (2) revisited. Abstract We compute the torsion-free linear maps J : su(2) → su(2), deduce a new determination of the integrable complex structures and their equivalence classes under the action of the automorphism group for u(2) and su(2) ⊕ su(2), and prove that in both cases the set of complex structures is a differentiable manifold. u(2) ⊕ u(2), su(2) N and u(2) N are also considered. Extension of complex structures from u(2) to su(2) ⊕ su(2) are studied, local holomorphic charts given, and attention is paid to what representations of u(2) we can get from a substitute to the regular representation on a space of holomorphic functions for the complex structure.
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Left invariant complex structures on U(2) and SU(2) × SU(2) revisited. ∗
Left invariant complex structures on U (2) and SU (2) × SU (2) revisited. Abstract We compute the torsion-free linear maps J : su(2) → su(2), deduce a new determination of the integrable complex structures and their equivalence classes under the action of the automorphism group for u(2) and su(2) ⊕ su(2), and prove that in both cases the set of complex structures is a differentiable manifold. u...
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