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Differential Geometry and its Applications, ISSN 0926-2245, 04/2015, Volume 39, pp. 147 - 165
I define higher codimensional versions of contact structures on manifolds as maximally non-integrable distributions. I call them multicontact structures.... 
[formula omitted]-algebras | Jets | Multisymplectic geometry | Contact geometry | Higher geometry | algebras | Algebra
Journal Article
International mathematics research notices, ISSN 1073-7928, 02/2019
Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about... 
Journal Article
Journal of Symplectic Geometry, ISSN 1527-5256, 2018, Volume 16, Issue 2, pp. 485 - 561
We show that a suitable notion of Dirac-Jacobi structure on a generic line bundle L, is provided by Dirac structures in the omni-Lie algebroid of L.... 
MATHEMATICS | POISSON MANIFOLDS | COISOTROPIC SUBMANIFOLDS | COMPLEX | OMNI-LIE ALGEBROIDS | LOCAL-STRUCTURE
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2014, Volume 16, Issue 6, pp. 1450007 - 1-1450007-49
It is well known that a foliation $\mathscr{F}$ of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e. leafwise)... 
characteristic cohomology | Lie-Rinehart algebras | Foliations | homotopy algebras | MATHEMATICS | LAGRANGIAN-FORMALISM | BRACKETS | MATHEMATICS, APPLIED | DEFORMATIONS | CONSERVATION-LAWS | C-SPECTRAL SEQUENCE | Algebra | Functions (mathematics) | Manifolds | Bundling | Brackets | Integrals | Mathematical analysis | Isomorphism | Fields (mathematics)
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2016, Volume 283, Issue 2, pp. 449 - 482
Geometric structures on NQ-manifolds, i.e., nonnegatively graded manifolds with a homological vector field, encode nongraded geometric data on Lie algebroids... 
Lie algebroids | Graded manifolds | Spencer operators | NQ-manifolds | Vector bundle valued differential forms | MATHEMATICS | graded manifolds | JACOBI STRUCTURES | vector bundle valued differential forms | GEOMETRY
Journal Article
Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 01/2015, Volume 158, Issue 1, pp. 155 - 191
... LieRinehart Algebras BY LUCA VITAGLIANO DipMat, Universit degli Studi di Salerno,& Istituto Nazionale di Fisica Nucleare, GC Salerno, Via Giovanni Paolo II n 123, 84084... 
MATHEMATICS | BRACKETS | COISOTROPIC SUBMANIFOLDS | COHOMOLOGY | GERSTENHABER ALGEBRAS | CATEGORY | DEFORMATIONS | MODULAR CLASS | BATALIN-VILKOVISKY ALGEBRAS | QUANTIZATION | Algebra | Calculus | Representations | Mathematical analysis | Manifolds (mathematics) | Lie groups
Journal Article
MATHEMATISCHE ZEITSCHRIFT, ISSN 0025-5874, 04/2020, Volume 294, Issue 3-4, pp. 1181 - 1225
This paper belongs to a series of works aiming at exploring generalized (complex) geometry in odd dimensions. Holomorphic Jacobi manifolds were introduced and... 
MATHEMATICS | Lie groupoid | DOUBLE LIE ALGEBROIDS | BUNDLES | Homogeneous Poisson structure | REDUCTION | Multiplicative tensor | DEFORMATIONS | Spencer operator | Holomorphic Jacobi structure | Holomorphic Poisson structure
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2015, Volume 17, Issue 2, pp. 1450026 - 1-1450026-34
An involutive distribution C on a smooth manifold M is a Lie-algebroid acting on sections of the normal bundle TM/C. It is known that the Chevalley–Eilenberg... 
characteristic cohomology | rings of differential operators | Foliations | universal enveloping algebras | homotopy algebras | LIE-ALGEBRAS | MATHEMATICS | LAGRANGIAN-FORMALISM | MATHEMATICS, APPLIED | GERSTENHABER | CONSERVATION-LAWS | C-SPECTRAL SEQUENCE | Algebra | Manifolds | Bundling | Operators | Associative | Integrals | Mathematical analysis | Fields (mathematics) | Representations
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 10/2014, Volume 11, Issue 9, pp. 1460039 - 1-1460039-35
Journal Article
Canadian journal of mathematics, ISSN 0008-414X, 10/2013, Volume 65, Issue 5, pp. 1164 - 1200
We define partial differential ( $\text{PD}$ in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and... 
Fiber bundles | Hamiltonian systems | Field theory | Multisymplectic geometry | fiber bundles | FIELDS | SYMMETRIES | CONSTRAINT ALGORITHM | CALCULUS | POISSON BRACKETS | FORMULATION | field theory | FORMS | MATHEMATICS | FORMALISM | MANIFOLDS | multisymplectic geometry | GEOMETRY
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 03/2012, Volume 9, Issue 2
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2010, Volume 60, Issue 6, pp. 857 - 873
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long... 
Geometry of PDEs | Lagrangian formalism | Field theory | Jet spaces | Hamiltonian formalism | MATHEMATICS | EQUATIONS | DYNAMICS | CONSERVATION-LAWS | FORMULATION | PHYSICS, MATHEMATICAL
Journal Article
Comptes Rendus Mathematique, ISSN 1631-073X, 04/2018, Volume 356, Issue 4, pp. 376 - 381
Let A⇒M be a Lie algebroid. In this short note, we prove that a pull-back of A along a fibration with homologically m-connected fibers shares the same... 
MATHEMATICS | MANIFOLDS
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2011, Volume 61, Issue 10, pp. 1932 - 1949
Diffieties formalize geometrically the concept of differential equations. We introduce and study Hamilton–Jacobi diffieties. They are finite dimensional... 
Geometry of PDEs | Lagrangian formalism | Fiber bundles | Diffieties | Hamilton–Jacobi theory | Hamiltonian formalism | Hamilton-jacobi theory | MATHEMATICS | Hamilton-Jacobi theory | FORMALISM | PHYSICS, MATHEMATICAL
Journal Article
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, ISSN 0219-8878, 03/2012, Volume 9, Issue 2, pp. 1260008 - 1260008
I review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles. 
jet spaces | PHYSICS, MATHEMATICAL | Hamilton-Jacobi theory | Lagrangian-Hamiltonian field theory | Field theory | Derivatives | Proposals | Bundles | Fibers
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 12/2010, Volume 7, Issue 8, pp. 1413 - 1436
We extend the geometric Hamilton-Jacobi formalism for Hamiltonian mechanics to higher-order field theories with regular Lagrangian density. We also investigate... 
Hamilton-Jacobi theory | Lagrangian-Hamiltonian field theory | Jet spaces | PHYSICS, MATHEMATICAL | GEOMETRY
Journal Article
Journal of Neuroscience, ISSN 0270-6474, 03/2008, Volume 28, Issue 11, pp. 2698 - 2709
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2009, Volume 59, Issue 4, pp. 426 - 447
Journal Article
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