arXiv subjects
Publications and source records attributed to Joseph Kwong.
We prove that a compact discrete quotient of a complex homogeneous space with compact isotropy is K\"ahler whenever it admits both a balanced metric and a pluriclosed metric. Moreover, if its real first Chern class vanishes, then the pluriclosed flow starting from any invariant pluriclosed metric exists for all time and converges smoothly to a flat K\"ahler metric.
We classify the left-invariant complex structures on the real Lie group SL(2,C) up to Lie group automorphism. The classification consists of the bi-invariant complex structure, a family parameterised by the unit disk, and one new, non-regular complex structure. The topology of the space of left-invariant complex structures (modulo automorphisms) is not Hausdorff. Finally, we show that the corresponding complex manifolds always admit left-invariant balanced metrics.
We characterise the existence of balanced and pluriclosed metrics on compact quotients of real semisimple Lie groups equipped with regular complex structures, in terms of Vogan diagrams. Consequently, such complex manifolds cannot simultaneously admit a balanced metric and a pluriclosed metric. Along the way, we revisit and correct the classification of regular complex structures on real semisimple Lie groups.