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Vanishing theorems for Hodge numbers and the Calabi curvature operator
Kyle Broder, Jan Nienhaus, Peter Petersen +2
It is shown that a compact -dimensional Kähler manifold with -positive Calabi curvature operator has the rational cohomology of complex projective space. For even $…
A general Schwarz lemma for Hermitian manifolds
Kyle Broder, James Stanfield
The Schwarz lemma for holomorphic maps between Hermitian manifolds is improved. New curvature constraints on the source and target manifolds are introduced and shown to be weaker t…
Some Remarks on the Wu--Yau Theorem
Kyle Broder
The Wu--Yau theorem asserts that a compact Kähler manifold with negative holomorphic sectional curvature admits a cohomologous metric with negative Ricci curvature. We introduce a…
--Quasi-Negative Curvature and Positivity of the Canonical Bundle
Kyle Broder, Kai Tang
A recent theorem of Diverio--Trapani and Wu--Yau asserts that a compact Kähler manifold with a Kähler metric of quasi-negative holomorphic sectional curvature is projective and can…
On the Gauduchon Curvature of Hermitian Manifolds
Kyle Broder, James Stanfield
It is shown that many results, previously believed to be properties of the Lichnerowicz Ricci curvature, hold for the Ricci curvature of all Gauduchon connections. We prove the exi…