activity
20212026
collaborators

8 papers

math.DG2026

T^2-invariant Einstein metrics on closed 4-manifolds

Kyle Broder, Ramiro A. Lafuente

We construct -invariant Einstein metrics with positive Ricci curvature on #_m(S^2 x S^2) for every integer . These provide infinite family of Einstein metrics on closed $…

math.DG2026

Curvature of hyperbolic complex manifolds

Kyle Broder, Hervé Gaussier

The article addresses the construction and geography of negatively curved metrics on hyperbolic complex manifolds. We introduce a mechanism for constructing complete Kähler metrics…

math.DG2026

Cohomogeneity-one Einstein metrics on closed -manifolds

Kyle Broder

We classify the Einstein metrics on closed 4-manifolds whose isometry group has dimension at least 3. Consequently, we show that the cohomogeneity-one Einstein metrics on a closed…

math.DG2025

Holomorphic -Contact and -Symplectic Line Bundles

Kyle Broder, Dan Popovici

We generalise the notions of scalar-valued holomorphic -contact and -symplectic structures introduced recently on compact complex manifolds by the second-named author jointly…

math.DG2025

Hyperbolicity and Schwarz Lemmas in Calibrated Geometry

Kyle Broder, Anton Iliashenko, Jesse Madnick

This paper has two main objectives. First, for an arbitrary calibrated manifold , we define notions of -hyperbolicity and -hyperbolicity, which respectively generali…

math.AG2024

Weakly Special Manifolds with no rational curves

Kyle Broder, Frédéric Campana

Assuming the abundance conjecture and the existence of a Zariski dense set of rational curves on terminal Calabi--Yau varieties, we show that a complex projective weakly special ma…

math.DG2023

Hermitian metrics with vanishing second Chern Ricci curvature

Kyle Broder, Artem Pulemotov

We describe a rigidity phenomenon exhibited by the second Chern Ricci curvature of a Hermitian metric on a compact complex manifold. This yields a characterisation of second Chern…

math.DG2021

Second-order estimates for collapsed limits of Ricci-flat Kähler metrics

Kyle Broder

We show that the singularities of the twisted Kähler--Einstein metric arising as the long-time solution of the Kähler--Ricci flow or in the collapsed limit of Ricci-flat Kähler met…