On the metric structure of non-Kähler complex surfaces

By F. Belgun. 2000

299 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/357f2fb99ac6c1ec59bb07963c25640b4f6bb3d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Morse–Novikov cohomology of locally conformally Kähler manifolds (2007, background): “On the other hand, it is shown in [11] that this solvmanifold is biholomorphic with an Inoue surface [8] which is known, [3], to not admit any Vaisman metric.”
The geometry of supersymmetric partition functions (2013, background): “See [80] for a discussion of metrics that have various other desirable properties.”
Bott–Chern cohomology of solvmanifolds (2012, background): “For instance, the geometry of nilmanifolds can be often reduced to the study of the associated Lie algebras, [21, 60, 14].”
Hermitian structures on six-dimensional nilmanifolds (2004, unknown): “Keywords: Hermitian structure, Kähler with torsion structure, balanced metric, locally conformal Kähler structure, generalized Hopf metric, nilmanifold MSC 2000: 53C55; 17B30, 32G05”
Geometric flow on compact locally conformally Kahler manifolds (2001, background): “See also [1] where a complete list of compact, complex surfaces admitting l.”
On cohomological decomposition of almost-complex manifolds and deformations (2009, background): “t there exists a symplectic form ωon M such that J is ω-tamed. Then one can consider (7) ˆω(X,Y) = Z M ω| p (Xp,Yp)η. ηbeing the volume form given in [25, lemma 6.2]. Then, it can be showed (see e.g. [5, 18]) that d ˆω= 0. Moreover, since Jis invariant, we have ωˆ(X,JX) = Z M ω| p (Xp,(JX)p)η = Z M ”
Vaisman metrics on solvmanifolds and Oeljeklaus–Toma manifolds (2012, background): “This Lie group G admits a left-invariant complex structure J and (G/Γ, J) admits a LCK metric but does not admit a Vaisman metric (see [6]).”
Balanced Hermitian structures on almost abelian Lie algebras (2020, methodology): “Recall that, by the symmetrization process described in [10, 22, 55], the existence of an SKT (resp.”
Strominger connection and pluriclosed metrics (2019, background): “When b1(M) is odd, Belgun gave in his beautiful work [3] a complete classification of all such metrics.”
On Eta-Einstein Sasakian Geometry (2004, methodology): “The Uniformization Theorem can now be stated as: Theorem 31 (Uniformization [ Bel00 ]).”
A survey on strong KT structures (2009, methodology): “For the balanced condition, by using a “symmetrization” process, which is based on a previous idea of Belgun [6], one has the following Theorem 2.2.”
On the evolution of a Hermitian metric by its Chern-Ricci form (2011, methodology): “If on the other handM is not Kähler, thanks to the Kodaira-Enriques classification [2, 3] we know that minimal non-Kähler compact complex surfaces fall into the following classes: 1) primary and secondary Kodaira surfaces, 2) surfaces of class VII with b2(M) = 0, 3) minimal surfaces of class VII wit”
Frankel conjecture and Sasaki geometry (2012, result): “When n = 1, our proof implies that any Sasaki structure on S3 is simple and its Kähler cone is C2\{0}; this result was proved by Belgun [2] as part of the classification of three dimensional Sasaki manifolds.”
Balanced Hermitian geometry on 6-dimensional nilmanifolds (2011, methodology): “The proof is based on the symmetrization process given in [2] (see also [9, 22]).”