Complex and Kähler structures on Compact Solvmanifolds

By K. Hasegawa. 2005

125 citations recorded by the source corpus.

We discuss our recent results on the existence and classification problem of complex and Kaehler structures on compact solvmanifolds. In particular, we determine in this paper all the complex surfaces which are diffeomorphic to compact solvmanifolds (and compact homogeneous manifolds in general).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cfd81e58d7df778cb9edc94b0c7c706da4b41398

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On Low-Dimensional Solvmanifolds (2009, background): “Even if a manifold has a complex structure, these conditions are not sufficient as the following theorem which is mentioned in [32] shows.”
A survey on strong KT structures (2009, background): “Moreover, in the case of solvmanifolds, Hasegawa proved in [27, 28] that a solvmanifold carries a Kähler metric if and only if it is covered by a finite quotient of a complex torus, which has the structure of a complex torus bundle over a complex torus.”
On the Chern‐Ricci flow and its solitons for Lie groups (2013, background): “Moreover, (J, ω) is a Kähler-Ricci soliton if and only if γ = 0 (expanding) and for γ = − (1)2 , the corresponding Lie group admits a lattice giving rise to a hermitian metric on an Inoue surface of type S0 which is an expanding CR-soliton when pulled back on its universal cover (see [8]).”
A correction to “Tamed symplectic forms and strong Kähler with torsion metrics” (2012, background): “, compact quotients of solvable Lie groups by discrete subgroups, Hasegawa showed in [24, 25] that a solvmanifold has a Kähler structure if and only if it is covered by a finite quotient of a complex torus, which has the structure of a complex torus bundle over a complex torus.”
Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures (2016, unknown): “The 4-dimensional solvmanifolds thus obtained are Inoue surfaces of type S (see [18]).”