An Obata-type characterization of Calabi metrics on line bundles
Nicolas Ginoux (IECL), Georges Habib, Mihaela Pilca (UR), Uwe, Semmelmann
TL;DR
This paper provides a characterization of Calabi metrics on line bundles by identifying specific properties of functions and Hessian structures on complete Kähler manifolds, advancing understanding of their geometric structure.
Contribution
It offers a new Obata-type characterization of Calabi metrics on line bundles through conditions on functions and Hessian eigenvalues.
Findings
Characterization of Calabi metrics via Hessian eigenvalues
Identification of conditions for functions with complex linear Hessian
Advancement in understanding Kähler manifold structures
Abstract
We characterize those complete K{\"a}hler manifolds supporting a nonconstant real-valued function with critical points whose Hessian is complex linear, has pointwise two eigenvalues and whose gradient is a Hessian-eigenvector.
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
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory