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

Izar, Alonso,; Salvatore, Francesca

doi:10.1007/s10455-021-09807-z

Cited by 3 publications

(1 citation statement)

References 30 publications

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“…(1.9) Balanced metrics were introduced in [Mic82] and provide a generalization of Kähler metrics, it has been extensively studied, see for instance [FP23] [BV17], [FGV19], [FLY12], [PPZ19], [AS22], and references therein. In this setting, we prove the following.…”

Section: Introductionmentioning

confidence: 99%

Levi-Civita Ricci-Flat Metrics on Non-Kähler Calabi-Yau Manifolds

Correa

2023

J Geom Anal

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We construct new examples of t-Gauduchon Ricci-flat metrics, for all t < 1, on compact non-Kähler Calabi-Yau manifolds defined by certain principal torus bundles over rational homogeneous varieties with Picard number ̺(X) > 1. As an application, we provide a detailed description of new examples of Strominger-Bismut Ricci-flat Hermitian metrics, Lichnerowicz Ricci-flat Hermitian metrics, and balanced Hermitian metrics on principal T 2 -bundles over the Fano threefold È(T È 2 ).

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Section: Introductionmentioning

confidence: 99%

Levi-Civita Ricci-Flat Metrics on Non-Kähler Calabi-Yau Manifolds

Correa

2023

J Geom Anal

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

Alonso,

Salvatore

2024

Ann Glob Anal Geom

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Coclosed $$G_2$$-structures on $$\text {SU}(2)^2$$-invariant cohomogeneity one manifolds

Alonso

2024

Ann Glob Anal Geom

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We consider two different $$\text {SU}(2)^2$$ SU ( 2 ) 2 -invariant cohomogeneity one manifolds, one non-compact $$M=\mathbb {R}^4 \times S^3$$ M = R 4 × S 3 and one compact $$M=S^4 \times S^3$$ M = S 4 × S 3 , and study the existence of coclosed $$\text {SU}(2)^2$$ SU ( 2 ) 2 -invariant $$G_2$$ G 2 -structures constructed from half-flat $$\text {SU}(3)$$ SU ( 3 ) -structures. For $$\mathbb {R}^4 \times S^3$$ R 4 × S 3 , we prove the existence of a family of coclosed (but not necessarily torsion-free) $$G_2$$ G 2 -structures which is given by three smooth functions satisfying certain boundary conditions around the singular orbit and a non-zero parameter. Moreover, any coclosed $$G_2$$ G 2 -structure constructed from a half-flat $$\text {SU}(3)$$ SU ( 3 ) -structure is in this family. For $$S^4 \times S^3$$ S 4 × S 3 , we prove that there are no $$\text {SU}(2)^2$$ SU ( 2 ) 2 -invariant coclosed $$G_2$$ G 2 -structures constructed from half-flat $$\text {SU}(3)$$ SU ( 3 ) -structures.

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

Cited by 3 publications

References 30 publications

Levi-Civita Ricci-Flat Metrics on Non-Kähler Calabi-Yau Manifolds

Levi-Civita Ricci-Flat Metrics on Non-Kähler Calabi-Yau Manifolds

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

Coclosed $$G_2$$-structures on $$\text {SU}(2)^2$$-invariant cohomogeneity one manifolds

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