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Lucio Bedulli

Publications and source records attributed to Lucio Bedulli.

At least 19 recordsLinked to original sources
arXiv2026

On homogeneous HKT manifolds and the Einstein condition

We consider homogeneous hypercomplex manifolds with a transitive action of a compact Lie group and we give a characterization of invariant HKT metrics on them. On every such hypercomplex manifold we prove the existence of an invariant HKT-Einstein metric, which is unique up to scaling. Furthermore, we determine for which invariant HKT metrics the torsion and the curvature of the Bismut connection are Bismut-parallel, showing that invariant strong HKT metrics have this property.

math.DG↗
arXiv2024

The behavior of the second Ricci flow on complex parallelizable manifolds

We study the flow of Hermitian metrics governed by the second Chern-Ricci form on a compact complex manifolds. The flow belongs to the family of Hermitian curvature flows introduced by Streets and Tian and it was considered by Lee in order to study compact Hermitian manifolds with almost negative Chern bisectional curvature. We show a regularity result on compact complex parallelizable manifolds and we prove that Chern-flat metrics are dynamically stable.

math.DG↗
arXiv2023

SYZ mirror symmetry of solvmanifolds

We present an effective construction of non-Kaehler supersymmetric mirror pairs in the sense of Lau,Tseng and Yau starting from left-invariant affine structures on Lie groups. Applying this construction we explicitly find SYZ mirror symmetric partners of all known compact 6-dimensional completely solvable solvmanifolds that admit a semi-flat type IIA structure.

math.DG↗
arXiv2023

The parabolic quaternionic Calabi-Yau equation on hyperkähler manifolds

We show that the parabolic quaternionic Monge-Ampère equation on a compact hyperkähler manifold has always a long-time solution which once normalized converges smoothly to a solution of the quaternionic Monge-Ampère equation. This is the same setting in which Dinew and Sroka prove the conjecture of Alesker and Verbitsky. We also introduce an analogue of the Chern-Ricci flow in hyperhermitian manifolds.

math.DG↗
arXiv2022

On the stability of the anomaly flow

We prove that the parabolic flow of conformally balanced metrics introduced by Phong, Picard and Zhang in "A flow of conformally balanced metrics with Kähler fixed points", is stable around Calabi-Yau metrics. The result shows that the flow can converge on a Kähler manifold even if the initial metric is not conformally Kähler.

math.DG↗
arXiv2021

A parabolic approach to the Calabi-Yau problem in HKT geometry

We consider the natural generalization of the parabolic Monge-Ampère equation to HKT geometry. We prove that in the compact case the equation has always a short-time solution and when the hypercomplex manifold is locally flat and admits a hyperkähler metric, then the equation has a long-time solution whose normalization converges to a solution of the quaternionic Monge-Ampère equation introduced by Alesker and Verbitsky. The result gives an alternative proof of a theorem of Alesker.

math.DG↗
arXiv2020

Stability of geometric flows of closed forms

We prove a general result about the stability of geometric flows of "closed" sections of vector bundles on compact manifolds. Our theorem allows to prove a stability result for the modified Laplacian coflow in G2-geometry introduced by Grigorian and for the balanced flow introduced by the authors in a previous paper.

math.DG↗
arXiv2018

A scalar Calabi-type flow in Hermitian Geometry: Short-time existence and stability

We introduce a new geometric flow of Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. The flow depends on the choice of a background metric, it always reduces to a scalar equation and preserves some special classes of Hermitian structures, as balanced and Gauduchon metrics. We show that the flow has always a unique short-time solution and we provide a stability result when the background metric is Kaehler-Einstein with nonpositive scalar curvature.

math.DG↗
arXiv2015

Second order geometric flows on foliated manifolds

We prove a general result about the short time existence and uniqueness of second order geometric flows transverse to a Riemannian foliation on a compact manifold. Our result includes some flows already existing in literature, as the transverse Ricci flow, the Sasaki-Ricci flow and the Sasaki J-flow and motivates the study of other evolution equations. We also introduce a transverse version of the Kaehler-Ricci flow adapting some classical results to the foliated case.

math.DG↗
arXiv2014

A parabolic flow of balanced metrics

We prove a general criterion to establish existence and uniqueness of a short-time solution to an evolution equation involving "closed" sections of a vector bundle, generalizing a method used recently by Bryant and Xu for studying the Laplacian flow in G_2-geometry. We apply this theorem in balanced geometry introducing a natural extension of the Calabi flow to the balanced case. We show that this flow has always a unique short-time solution belonging to the same Bott-Chern cohomology class of the initial balanced structure and that it preserves the Kaehler condition. Finally we study explicitly the flow on the Iwasawa manifold.

math.DG↗
arXiv2007

Torsion of SU(2)-structures and Ricci curvature in dimension 5

In anlogy with the work of R. Bryant on the Ricci tensor of a G$_2$-structure, we study the intrinsic torsion of an SU$(2)$-structure on a 5-dimensional manifold deriving an explicit expression for the Ricci and the scalar curvature in terms of torsion forms and its derivative. As a consequence of this formula we prove that the $α$-Einstein condition forces some special SU(2)-structures to be Sasaki-Einstein.

math.DG↗
arXiv2006

The Ricci tensor of SU(3)-manifolds

Following the approach of Bryant we study the intrinsic torsion of a SU(3)-manifold deriving a number of formulae for the Ricci and the scalar curvature in terms of torsion forms. As a consequence we prove that in some special cases the Einstein condition forces the vanishing of the intrinsic torsion.

math.DG↗
arXiv2006

Homogeneous Lagrangian submanifolds

We characterize isometric actions on compact Kaehler manifolds admitting a Lagrangian orbit, describing under which condition the Lagrangian orbit is unique. We furthermore give the complete classification of simple groups acting on the complex projective space with a Lagrangian orbit, and we give the explicit list of these orbits.

math.DG↗