Izar Alonso

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math.DG2025

Gauge theory on $T^{*} C P^{2}$ : explicit Sp(2)-instantons, HYM connections, and Spin(7)-instantons

Izar Alonso, Jesse Madnick, Emily Autumn Windes

We construct and classify $S U (3)$ -invariant primitive Hermitian Yang-Mills connections and $S p (2)$ -instantons with gauge groups $S = S^{1}$ and $S = S O (3)$ over the Calabi manifold $…

math.DG2025

On the existence of balanced metrics on six-manifolds of cohomogeneity one

Izar Alonso, Francesca Salvatore

We consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced $SU (n)$ -structures. Such structures are of int…

math.DG2024

Coclosed $G_{2}$ -structures on $SU (2)^{2}$ -invariant cohomogeneity one manifolds

Izar Alonso

We consider two different $SU (2)^{2}$ -invariant cohomogeneity one manifolds, one non-compact $M = R^{4} \times S^{3}$ and one compact $M = S^{4} \times S^{3}$ , and study the exis…

math.DG2024

New examples of $G_{2}$ -instantons on $R^{4} \times S^{3}$

Izar Alonso

We study the existence of $SU (2)^{2}$ -invariant $G_{2}$ -instantons on $R^{4} \times S^{3}$ with the coclosed $G_{2}$ -structures found on [arXiv:2209.02761]. We find an explic…

Gauge theory on T∗CP2: explicit Sp(2)-instantons, HYM connections, and Spin(7)-instantons

On the existence of balanced metrics on six-manifolds of cohomogeneity one

Coclosed G2​-structures on SU(2)2-invariant cohomogeneity one manifolds

New examples of G2​-instantons on R4×S3

Gauge theory on $T^{*} C P^{2}$ : explicit Sp(2)-instantons, HYM connections, and Spin(7)-instantons

Coclosed $G_{2}$ -structures on $SU (2)^{2}$ -invariant cohomogeneity one manifolds

New examples of $G_{2}$ -instantons on $R^{4} \times S^{3}$