arXiv research

We propose a new definition of so called Hamiltonian forms in n-plectic geometry and show that they have a non-trivial Lie infinity-algebra structure.

A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n+1. In our previous work with Baez and Hoffnung, we described how the `higher analogs' of the algebraic and geometric structures found in symplectic geometry should naturally arise i…

This paper associates homotopy Poisson-n algebras to higher symplectic structures.

We define an n-plectic structure as a commutative and torsionless Lie Rinehart pair, together with a distinguished cocycle from its Chevalley-Eilenberg complex. This 'n-plectic cocycle' gives rise to an extension of the Chevalley-Eilenberg complex by so called symplectic tensors. The cohomology of this extension genera…

Unified framework for observables in n-plectic geometry.

We consider generalizations of symplectic manifolds called n-plectic manifolds. A manifold is n-plectic if it is equipped with a closed, nondegenerate form of degree n+1. We show that higher structures arise on these manifolds which can be understood as the categorified or homotopy analogues of important structures stu…

We investigate Nijenhuis deformations of $L_\infty$-algebras, a notion that unifies several Nijenhuis deformations, namely those of Lie algebras, Lie algebroids, Poisson structures and Courant structures. Additional examples, linked to Lie $n$-algebras and $n$-plectic manifolds, are included.

This Master Thesis is devoted to the study of $n$-plectic manifolds and the Strongly Homotopy Lie algebras, also called $L_{\infty}$-algebras, that can be associated to them. Since multisymplectic geometry and $L_{\infty}$-algebras are relevant in Theoretical Physics, and in particular in String Theory, we introduce th…

The paper introduces a new form on Lie algebroids over multisymplectic manifolds.

In the first chapter, we give a precise and general description of gerbes valued in arbitrary crossed module and over an arbitrary differential stack. We do it using only Lie groupoids, hence ordinary differential geometry, by considering differential stacks as being Lie groupoids up to Morita equivalence. We prove the…

Defines compatibility between Riemannian and Jacobi structures.

The paper introduces new structures for left-symmetric algebroids.

Defines compatibility between Riemannian and Jacobi structures.

Extending Jacobi and Riemannian compatibility to Lie algebroids.

Study projective and direct limits of Banach structures with connections to $G$-structures.

Defines structure constants for specific geometric structures on Lie groups.

Study on $G_2^*$ structures and almost para-contact structures in 7D.

Defines a new Poisson structure for generalized Sasakian spaces.

Study on types of generalized hypercomplex structures on tori and Kodaira-Thurston surface.

Classifies complex Dirac structures with invariants and local structure.

Study $G_2$ structures on manifolds to find specific almost contact metric structures.

This article connects PCS structures to parabolic contact structures.

Bihamiltonian structures lead to tau structures for integrable hierarchies.

The paper explores geometric structures on Hom-Lie groups and algebras.

Extends corner structure study to general case, constructs normal Trans-Sasakian structures.

Study on submanifolds in metallic structures with new results and structures.

New metric structures generalize Sasakian and cosymplectic structures, proving rigidity and finding conditions.

Study $GL(2)$-structures on manifolds leading to complex structures.

3D projective structures can be metrized with conformal structures.

Hypersymplectic structures with torsion on Lie algebroids are investigated. We show that each hypersymplectic structure with torsion on a Lie algebroid determines three Nijenhuis morphisms. From a contravariant point of view, these structures are twisted Poisson structures. We prove the existence of a one-to-one corres…

Spin-harmonic structures on low-dimensional manifolds.

Study equivalence between Hessian and Born structures on tangent bundles.

New geometric structure on surfaces generalizing complex structures.

Introduces compatibility between Dirac structures and Nijenhuis tensors.

Conditions for hypersurfaces of generalized Kähler manifolds to have specific structures are established.

New G2-structures found on Lie groups with strong structural conditions.

We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact structures. We obtain a generalized Sasakian structure on a non-compact manifold which…

Introduces semi-abelian generalized complex structures.

Introduces VB-structures for geometric objects on manifolds.

New Clifford-Weyl structures defined on conformal manifolds.

The paper studies nilpotent structures in oriented neutral vector bundles and neutral hyperKähler structures.

Contact structures on manifolds linked to cone structures.

New complex orthogonal structures found on a 3D manifold.

Spin-structures on real Bott manifolds with Kähler structure are characterized.

Study ${ m SU}(3)$-structures and their relation to supersymmetry.

Exotic hypercomplex structures on a torus are proven to not exist.

Global Poisson structures on $S^4$ studied using twistor methods.

Unique birational structure proven on Inoue surfaces.