scholarly journals Dolbeault and J-Invariant Cohomologies on Almost Complex Manifolds

2021 ◽  
Vol 15 (7) ◽  
Author(s):  
Lorenzo Sillari ◽  
Adriano Tomassini
Keyword(s):  
Complex Manifold ◽  
Sufficient Condition ◽  
Complex Manifolds ◽  
Necessary And Sufficient Condition ◽  
Dolbeault Cohomology ◽  
Almost Complex Manifolds ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Necessary And Sufficient

AbstractIn this paper we relate the cohomology of J-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given.

scholarly journals The union problem on complex manifolds

2002 ◽  
Vol 30 (10) ◽  
pp. 621-625
Author(s):  
Patrick W. Darko
Keyword(s):  
Complex Manifold ◽  
Sufficient Condition ◽  
Complex Manifolds ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

LetΩbe a relatively compact subdomain of a complex manifold, exhaustable by Stein open sets. We give a necessary and sufficient condition forΩto be Stein, in terms ofL2-estimates for the∂¯-operator, equivalent to the condition of Markoe (1977) and Silva (1978).

The Tangent Bundle of an Almost Complex Manifold

2001 ◽  
Vol 44 (1) ◽  
pp. 70-79 ◽  
Author(s):  
László Lempert ◽  
Róbert Szőke
Keyword(s):  
Complex Manifold ◽  
Tangent Bundle ◽  
Deformation Theory ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Holomorphic Maps ◽  
Almost Complex Manifolds ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Natural Way

AbstractMotivated by deformation theory of holomorphic maps between almost complex manifolds we endow, in a natural way, the tangent bundle of an almost complexmanifold with an almost complex structure. We describe various properties of this structure.

scholarly journals ON THE COHOMOLOGY OF ALMOST-COMPLEX MANIFOLDS

2012 ◽  
Vol 23 (02) ◽  
pp. 1250019 ◽  
Author(s):  
DANIELE ANGELLA ◽  
ADRIANO TOMASSINI
Keyword(s):  
Complex Structure ◽  
Almost Complex Structure ◽  
Complex Manifolds ◽  
Almost Complex Manifolds ◽  
Dynamical Study ◽  
Almost Complex Manifold ◽  
Almost Complex ◽  
Kähler Structures ◽  
Foliated Manifolds ◽  
Invent Math

Following [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683] and the results obtained by [D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math.36(1) (1976) 225–255] to study the cone of semi-Kähler structures on a compact semi-Kähler manifold.

Adapted connections on Kaehler–Norden Golden manifolds and harmonicity

2020 ◽  
Vol 17 (02) ◽  
pp. 2050027
Author(s):  
Rakesh Kumar ◽  
Garima Gupta ◽  
Rachna Rani
Keyword(s):  
Harmonic Map ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Almost Complex ◽  
Set Up ◽  
Necessary And Sufficient ◽  
Hessian Metric

We study almost complex Norden Golden manifolds and Kaehler–Norden Golden manifolds. We derive connections adapted to almost complex Norden Golden structure of an almost complex Norden Golden manifold and of a Kaehler–Norden Golden manifold. We also set up a necessary and sufficient condition for the integrability of almost complex Norden Golden structure. We define twin Norden Golden Hessian metric for a Kaehler–Norden Golden Hessian manifold. Finally, we prove that a complex Norden Golden map between Kaehler–Norden Golden manifolds is a harmonic map.

scholarly journals Dolbeault cohomology for almost complex manifolds

2021 ◽  
Vol 391 ◽  
pp. 107970
Author(s):  
Joana Cirici ◽  
Scott O. Wilson
Keyword(s):  
Complex Manifolds ◽  
Dolbeault Cohomology ◽  
Almost Complex Manifolds ◽  
Almost Complex

EXAMPLES OF COMPACT NEGATIVELY CURVED ALMOST COMPLEX, BUT NOT COMPLEX, MANIFOLDS

2012 ◽  
Vol 09 (07) ◽  
pp. 1220012
Author(s):  
JIN HONG KIM
Keyword(s):  
Complex Manifold ◽  
Betti Number ◽  
Homology Group ◽  
Complex Manifolds ◽  
Almost Complex Manifold ◽  
Negatively Curved ◽  
Complex Dimension ◽  
Almost Complex ◽  
Homogeneous Domains

In this paper, we provide infinitely many examples of compact negatively curved almost complex, but not complex, manifolds of complex dimension 2n + 1 or 2n + 2 by using strongly pseudoconvex homogeneous domains in an almost complex manifold. Unlike the Kodaira–Thurston manifold which is the flat case, the first Betti number of the constructed manifolds is even, and their first homology group is, in fact, isomorphic to ℤ4n+2 or ℤ4n+4.

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.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

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