Bari-Salerno Differential Geometry Days

February 9-11, 2026, DipMat, University of Salerno

 

The meeting revolves around the research interests of the Differential Geometry Groups of the Universities of Bari and Salerno, namely: geometric structures on Riemannian manifolds, particularly almost contact and related structures, including their relation to complex and related structures, connections and curvature; geometry and topology of Sasakian, lcK and related manifolds, G-structures and Cartan structures; Poisson geometry, Lie groupoids, Lie algebroids and differentiable stacks; deformation theory, deformation quantization,  reduction and formality. The main aim of the meeting is promoting the collaboration between the two groups involved at different levels.

 

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Participants

 

Alessandro Carotenuto (University of Parma)

Margherita D’Alessandro (University of Bari)

Francesco D’Andrea (University of Napoli “Federico II”)

Antonio De Nicola (University of Salerno)

Giulia Dileo (University of Bari)

Dario Di Pinto (University of Bari)

Chiara Esposito (University of Salerno)

Matthijs Lau (University of Salerno)

Antonio Maglio (IMPAN, Warsaw)

Antonio M. Miti (Unversity of Rome “La Sapienza”)

Maria Assunta Squillante (University of Salerno)

Alfonso G. Tortorella (University of Salerno)

Luca Vitagliano (University of Salerno)

Alessandro Zampini (University of Napoli “Federico II”)

 

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Schedule

 

The meeting will take place in the following rooms (see the schedule below)

 

MR – meeting room of the DipMat, Fisciano Campus, F2 building, 1^st floor.

F3 – room F3, Fisciano Campus, F2 building, ground floor.

 

The following schedule is tentative and may be subject to (significant) changes!

 

	Mon 9 – room MR	Tue 10 – room F3	Wed 11 – room MR
09:00 - 09:50		Di Pinto
10:00 -  10:50	Dileo	Tortorella	De Nicola
	break	break	break
11:30 - 12:20	Dileo	Tortorella	D’Alessandro
12:30 -  13:20	Esposito	Maglio	Lau
	lunch	lunch	lunch
15:30 -  16:20	Vitagliano	Discussions
16:30 -  17:20	Vitagliano	Discussions
		social dinner

 

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Titles and Abstracts

 

Margherita D’Alessandro (1 hr)

Title: On 7-Dimensional Almost 3-Contact Metric Manifolds and G₂-Structures

Abstract: The existence of a G₂-structure on a 7-dimensional manifold is a topological property equivalent to the reduction of the structure group to the exceptional Lie group G₂. This can be characterized by the existence of a unit spinor or, equivalently, a stable 3-form. Such structures arise naturally when the manifold admits an almost 3-contact metric structure (A3CM), corresponding to a further reduction of the structure group to Sp(1) ⊂ G₂. In this talk, I will survey the interplay between these two structures, which has been studied extensively in recent years [1],[2]. I will focus on particular classes of A3CM manifolds, like the 3-Sasakian case, where the associated G₂-structure belongs to specific classes of the Fernández-Gray classification [3]. Finally, I will discuss the most general setting, focusing on the intrinsic torsion of the G₂-structure and showing how it can be described in terms of the underlying contact structures.

 

References

[1] I. Agricola and G. Dileo. Generalization of 3-Sasakian manifolds and skew torsion, Adv. Geom. 20 (2020), 331–374.

[2] I. Agricola and T. Friedrich. 3-Sasakian manifolds in dimension seven, their spinors and G2 structures, J. Geom. Phys. 60 (2010), 326–332.

[3] M. Fernández and A. Gray. Riemannian manifolds with structure group G2, Ann. Mat. Pura Appl. 132 (1982), 19–45.

 

 

Antonio De Nicola (1 hr)

Title: Darboux-Lie Derivatives: a Unified Calculus for G-Structures

Abstract: In the theory of G-structures on manifolds, geometric structures are often described in terms of gauge equivalence classes of soldering forms. However, a comprehensive calculus of derivatives for such forms and their gauge transformations has been lacking. In this talk, based on joint work with Ivan Yudin, I will introduce the concept of the Darboux-Lie derivative, a new tool designed to fill this gap.

We define the Darboux-Lie derivative for fiber bundle maps from natural bundles to associated fiber bundles. This construction generalizes the “metamathematical” notion of a derivative, utilizing the Trautman lift as a very general framework. I will demonstrate how this single operator unifies various classical concepts, showing that the standard Lie derivative, the covariant derivative, and the classical Darboux derivative for group valued maps are all specific instances of the Darboux-Lie derivative.

Key properties of this new derivative will be discussed, including:

• Its behavior on products, tensor products, and compositions (Leibniz and chain rules).

• Its expression in terms of flows.

• The derivation of a Cartan-type magic formula for the covariant Darboux-Lie derivative.

Finally, I will briefly outline applications to G-structures, specifically how this derivative characterizes infinitesimal automorphisms and torsion-free conditions.

 

 

Giulia Dileo (2 hrs)

Title: An Introduction to the Geometry of Almost Contact and Almost 3-Contact Metric Manifolds

Abstract: Almost contact metric manifolds are a broad class of manifolds providing an odd dimensional counterpart to almost Hermitian geometry. An integrability condition in this context is given by normality, which is satisfied by remarkable classes such as Sasakian, coKähler and Kenmotsu manifolds. In this talk I will describe fundamental examples and properties of almost contact metric manifolds, including the transverse geometry with respect to the orbits of the Reeb vector field. The second part will be concerned with almost 3-contact metric manifolds, endowed with three structures satisfying suitable compatibility conditions. In fact they provide an odd-dimensional counterpart to almost hyperHermitian manifolds. I will describe the class of 3-(α, δ)-Sasaki manifolds which generalize 3-Sasaki manifolds, and which admit local Riemannian submersions over quaternionic Kähler manifolds. A fundamental tool in studying these structures is given by a canonical metric connection with totally skew-symmetric torsion.

 

 

Dario Di Pinto (1 hr)

Title: On the Classification of Almost Contact Metric Manifolds with Applications to Connections with Torsion

Abstract: Metric connections with totally skew-symmetric torsion play a central role in the study of Riemannian manifolds endowed with special geometric structures. Indeed, in many cases, the Levi-Civita connection fails to preserve the underlying geometric structure, making it natural to consider a more suitably adapted connection. Owing to their properties, metric connections with skew-symmetric torsion provide an effective alternative to the Levi-Civita connection.

Within the framework of almost contact metric geometry, the existence of an adapted metric connection with totally skew-symmetric torsion – known as the characteristic connection – was characterized by T. Friedrich and S. Ivanov [2]. In this talk I will present a new characterization in terms of the Chinea-Gonzalez classes, as it happens for almost-Hermitian manifolds and G2-manifolds. This result is obtained through a new classification scheme for a wide class of almost contact metric structures, called H-parallel, together with the introduction of the class Cmin that fully describes H-parallel structures whose intrinsic torsion is totally skew-symmetric.

In the final part of the talk I will focus on C_min-manifolds and discuss some of their geometric properties.

 

References

[1] I. Agricola, D. Di Pinto, G. Dileo, M. Kuhrt, A new approach to the classification of almost contact metric manifolds via intrinsic endomorphisms (2025), preprint.

[2] T. Friedrich, S. Ivanov, Parallel spinors and connections with skew-symmetric torsion in string theory, Asian J. Math. 6 (2002), 303-335.

 

 

Chiara Esposito (1 hr)

Title: Deformation Quantization via Formality, and Beyond: Symmetries and Reduction

Abstract: In this introductory seminar, I will present the basic ideas of deformation quantization as a framework for passing from classical to quantum mechanics by deforming the commutative algebra of functions on a Poisson manifold into a noncommutative star-product algebra. After recalling the role of Poisson brackets and the guiding principles behind star products, I will outline the statement and significance of the Formality Theorem, which provides a conceptual bridge between Poisson geometry and associative deformations via an L-infinity-quasi-isomorphism. I will conclude with a brief overview of my current research directions, focusing on the interplay between symmetries and quantization.

 

 

Matthijs Lau (1 hr)

Title: Multiplicative Ehresmann Connections

Abstract: In this talk, we will extend the notion of multiplicative Ehresmann connection, as introduced on Lie groupoid extensions by Fernandes and Marcut, to general surjective submersions of Lie groupoids, and see how these incorporate a fibrewise compatibility. In particular, this unifies many familiar notions of connections: affine connections, principal connections, and multiplicative Ehresmann connections. Our main interests lie in the existence and completeness of these objects. Therefore, we will start with a short overview of related results for Lie groupoid extensions and fibre bundles. Then we will see how we can emulate some of these results for particular classes of morphisms, in particular, Lie groupoid fibrations and families of Lie groupoids, and the connections between them.

 

 

Antonio Maglio (1 hr)

Title: Lie Groupoids and Differentiable Stacks

Abstract: Differentiable stacks are geometric objects that model singular spaces such as orbit spaces of Lie group actions, orbifolds, and leaf spaces of foliations. They can be described as equivalence classes of Lie groupoids up to Morita equivalence.

In this talk, I will give an overview of differentiable stacks and their geometry. I will begin by recalling the notions and some examples of Lie groupoids, Morita equivalence, and differentiable stacks. I will then discuss geometric structures in the setting of Lie groupoids and differentiable stacks, with a focus on vector bundles and differential forms.

 

 

Alfonso G. Tortorella (2 hr)

Title: Deformations of Coisotropic Submanifolds: An Overview

Abstract: Coisotropic submanifolds play a relevant role in symplectic geometry and mathematical physics, for instance they allow to perform symplectic reduction and describe Hamiltonian systems with symmetries or constraints. The deformation problem of coisotropic submanifolds has been first studied in the symplectic setting by Oh & Park with original motivation coming from the seminal work of Kapustin & Orlov in Homological Mirror Symmetry. After that, the coisotropic deformation problem has been also studied in the setting of Poisson manifolds (Schaetz & Zambon), locally conformally symplectic manifolds (Le & Oh), and contact/Jacobi manifolds (Oh, Le, AGT & Vitagliano). The aim of the talk is to give an overview of the deformation problem of coisotropic submanifolds, mainly in the symplectic setting for easiness of presentation.

 

 

Luca Vitagliano (2 hr)

Title: The Symplectic-to-Contact Dictionary

Abstract: There is a dictionary that allows to translate from symplectic-related geometries to contact-related geometries. When applied to Poisson structures, the dictionary gives back Jacobi structures, and when applied to complex structures, it gives back normal almost contact structures. The dictionary is an efficient tool in Contact Geometry as, in principle, it can be efficiently used to state and prove theorems from their analogues in Symplectic Geometry. I will present two versions of the dictionary and discuss a range of possible applications.

 

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More Information

 

For more information or to attend the meeting please send an e-mail to: lvitagliano@unisa.it