TL;DR
This paper introduces harmonic complex structures, a new geometric concept that generalizes Kähler structures by using harmonic theory on vector bundle-valued differential forms, bridging complex and Kähler geometries.
Contribution
It proposes harmonic complex structures as a novel intermediate between complex and Kähler structures, extending differential geometric frameworks.
Findings
Harmonic complex structures generalize Kähler structures
They are defined via harmonic theory on vector bundle-valued forms
This new concept bridges complex and Kähler geometries
Abstract
In this paper, we introduce a new concept so called harmonic complex structure by using harmonic theory for vector bundle-valued differential forms. It is a new structure intermediates between complex structure and K\"ahler structure. From differential geometric viewpoint, it is a natural generalization of K\"ahler structure.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research