The Schwarz lemma in K\"ahler and non-K\"ahler geometry
Kyle Broder
TL;DR
This paper introduces new curvature notions to refine the Schwarz lemma in both Kähler and non-Kähler geometries, unifying various forms and deriving new Schwarz lemmas in Hermitian and Kähler contexts.
Contribution
It presents two new curvatures that clarify existing concepts and offers a unified framework for Schwarz lemmas across different geometric categories.
Findings
New curvatures refine real bisectional curvature
Unified perspective leads to novel Schwarz lemmas
Results apply to both Kähler and Hermitian geometries
Abstract
We introduce two new curvatures which refine and elucidate the real bisectional curvature considered by Yang-Zheng \cite{YangZheng}. A unified perspective of the various forms of the Schwarz lemma is given, leading to novel Chern-Lu, Aubin-Yau, and Chen-Cheng-Look Schwarz lemmas in both the K\"ahler and Hermitian category.
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Taxonomy
TopicsGeometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows