Complex analytic geometry of complex parallelizable manifolds
We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.
For a complex solvable Lie group acting holomorphically on a Kähler manifold every closed orbit is isomorphic to a torus and any two such tori are isogenous. We prove a similar result for singular Kähler spaces.
We determine which algebraic surface of logarithmic irregularity admit an algebraically non-degenerate entire curve.
We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.
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