An almost pluriclosed flow

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Masaya Kawamura
Keyword(s):  
Evolution Equations ◽  
Curvature Flow ◽  
Almost Complex Manifolds ◽  
Hermitian Manifolds ◽  
Almost Complex ◽  
Almost Hermitian Manifolds ◽  
Parabolic Evolution Equations ◽  
Hermitian Curvature Flow ◽  
Parabolic Flows ◽  
The Relationship

AbstractWe define two parabolic flows on almost complex manifolds, which coincide with the pluriclosed flow and the Hermitian curvature flow respectively on complex manifolds.We study the relationship between these parabolic evolution equations on compact almost Hermitian manifolds.

scholarly journals Almost Hermitian Identities

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1357
Author(s):  
Joana Cirici ◽  
Scott O. Wilson
Keyword(s):  
Commutation Relation ◽  
Complex Manifold ◽  
Exterior Differential ◽  
Almost Complex Manifold ◽  
Hermitian Manifolds ◽  
Almost Complex ◽  
Almost Hermitian Manifolds

We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we obtain generalizes the backbone of the local Kähler identities to the setting of almost Hermitian manifolds, allowing for new global results for such manifolds.

scholarly journals On Kähler-like and G-Kähler-like almost Hermitian manifolds

2020 ◽  
Vol 7 (1) ◽  
pp. 145-161
Author(s):  
Masaya Kawamura
Keyword(s):  
Complex Structure ◽  
Hermitian Manifold ◽  
Almost Complex Structure ◽  
Almost Hermitian Manifold ◽  
Hermitian Manifolds ◽  
Almost Complex ◽  
Almost Hermitian Manifolds ◽  
Balanced Metric

AbstractWe introduce Kähler-like, G-Kähler-like metrics on almost Hermitian manifolds. We prove that a compact Kähler-like and G-Kähler-like almost Hermitian manifold equipped with an almost balanced metric is Kähler. We also show that if a Kähler-like and G-Kähler-like almost Hermitian manifold satisfies B_{\bar i\bar j}^\lambda B_{\lambda j}^i \ge 0, then the metric is almost balanced and the almost complex structure is integrable, which means that the metric is balanced. We investigate a G-Kähler-like almost Hermitian manifold under some assumptions.

scholarly journals On the cohomology of almost-complex and symplectic manifolds and proper surjective maps

2016 ◽  
Vol 27 (12) ◽  
pp. 1650103 ◽  
Author(s):  
Nicoletta Tardini ◽  
Adriano Tomassini
Keyword(s):  
Symplectic Manifolds ◽  
Complex Manifolds ◽  
Cohomology Groups ◽  
Almost Complex Manifolds ◽  
Almost Complex Manifold ◽  
Dimension Formula ◽  
Almost Complex ◽  
De Rham ◽  
The Relationship

Let [Formula: see text] be an almost-complex manifold. In [Comparing tamed and compatible symplectic cones and cohomological properties of almost-complex manifolds, Comm. Anal. Geom. 17 (2009) 651–683], Li and Zhang introduce [Formula: see text] as the cohomology subgroups of the [Formula: see text]th de Rham cohomology group formed by classes represented by real pure-type forms. Given a proper, surjective, pseudo-holomorphic map between two almost-complex manifolds, we study the relationship among such cohomology groups. Similar results are proven in the symplectic setting for the cohomology groups introduced in [Cohomology and Hodge Theory on Symplectic manifolds: I, J. Differ. Geom. 91(3) (2012) 383–416] by Tseng and Yau and a new characterization of the hard Lefschetz condition in dimension [Formula: see text] is provided.

scholarly journals Differential operators on almost-Hermitian manifolds and harmonic forms

2020 ◽  
Vol 7 (1) ◽  
pp. 106-128 ◽  
Author(s):  
Nicoletta Tardini ◽  
Adriano Tomassini
Keyword(s):  
Differential Operators ◽  
Hodge Theory ◽  
Harmonic Forms ◽  
Hermitian Manifolds ◽  
Almost Complex ◽  
Almost Hermitian Manifolds ◽  
De Rham ◽  
Almost Kähler ◽  
Associated Spaces ◽  
Cohomological Interpretation

AbstractWe consider several differential operators on compact almost-complex, almost-Hermitian and almost-Kähler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces of harmonic forms and cohomologies with the classical de Rham, Dolbeault, Bott-Chern and Aeppli cohomologies.

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