On astheno-Kähler manifolds

2025/06/04 by Gupta, Punam, Yadav, Nidhi · 1 citation
#32C35 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.06369

Abstract

This survey explores a range of classical findings and recent developments related to our understanding of astheno-Kähler manifolds. Furthermore, we provide various examples of astheno-Kähler manifolds and analyze the challenges associated with their existence.

Citations

• Semi-stable twisted holomorphic vector bundles over Gauduchon manifolds
• Deformations of astheno-Kähler metrics
• Remarks on astheno-Kahler manifolds, Bott-Chern and Aeppli cohomology groups
• On cohomological and formal properties of Strong Kähler with torsion and astheno-Kähler metrics
• Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics
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• The Fu-Yau equation on compact astheno-Kähler manifolds
• Positive projectively flat manifolds are locally conformally flat-Kähler Hopf manifolds
• Homogeneous Hermitian manifolds and special metrics
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• Hermitian-Einstein connections on principal bundles over flat affine manifolds
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• A parabolic flow of pluriclosed metrics

Cited by

• Harmonicity of the complex structure on product of trans-Sasakian manifolds

Related

• Explicit Constructions of Astheno-Kähler Manifolds
• Remarks on astheno-Kahler manifolds, Bott-Chern and Aeppli cohomology groups
• Hyperkähler manifolds
• Astheno-Kähler and balanced structures on fibrations
• On cohomological and formal properties of Strong Kähler with torsion and astheno-Kähler metrics