A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The polysymplectic (n+1)-form is introduced as an analogue of the symplectic form for the De Donder-Weyl polymomentum Hamiltonian formulation of field theory. The corresponding Poisson brackets on differential forms are constructed. The analogues of the Poisson algebra are shown to be generalized (non-commutative and…
We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.
A description of classical field theories of first order in terms of Lagrangian submanifolds of premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated with a fibration is discussed. The triple is adapted to the extended Hamiltonian formalism. Using this triple, we prove that Euler-…
Canonical structure of the space-time symmetric analogue of the Hamiltonian formalism in field theory based on the De Donder-Weyl (DW) theory is studied. In n space-time dimensions the set of n polymomenta is associated to the space-time derivatives of field variables. The polysymplectic (n+1)-form generalizes th…
The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try to stress out the interplay between the Lepage-Dedecker (LP) description and the …
The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle J1∗(T,M) (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize our approach of multi-time Hamilton geometry. In this direction, we firstly intro…
The paper extends Hodge-de Rham theory to higher-dimensional Sierpinski gaskets.
problem Analyzing differential forms and Laplacians on higher-dimensional fractal structures.
method Constructing sequences of graphs approximating Sierpinski gaskets, defining k-forms, de Rham derivatives, and their duals, proving harmonic properties, and exploring 2-forms.
result Obtained a basis for the space of harmonic 1-forms on level-3 Sierpinski gasket.
Paper introduces a new multilinear functional for spectral triples and computes its properties.
problem Computing properties of spectral triples and their associated Hodge operators.
method Introduces a new multilinear functional for spectral triples and computes its properties using noncommutative residue and perturbed de-Rham Hodge operators.
result Recover two forms, torsion of the linear connection, and four forms by the noncommutative residue and perturbed de-Rham Hodge Dirac triple.
On every compact, orientable, irreducible 3-manifold V which is toroidal or has torus boundary components we construct a contact 1-form whose Reeb vector field R does not have any contractible periodic orbits and is tangent to the boundary. Moreover, if bdry V is nonempty, then the Reeb vector field R is transverse to …
On any compact manifold of dimension greater than 6, we prescribe the volume and any finite part of the spectrum Hodge Laplacian acting on p-form for 1≤p<2n. In particular, we prescribe the multiplicity of the first eigenvalues.
The paper extends Hodge-de Rham and Lichnérowicz Laplacians to double forms and proves vanishing theorems.
problem Extending Laplacians to double forms and proving vanishing theorems.
method Introduced a new product on double forms to establish index-free formulas for curvature terms in Weitzenböck formulas for Δ, Δ, and ΔL. Proved vanishing theorems for Δ and ΔL on symmetric double forms.
result Vanishing theorems for the Hodge-de Rham Laplacian and ΔL on symmetric double forms.
A classical result in differential geometry states that for a free and proper Lie group action, the quotient map to the orbit space induces an isomorphism between the de Rham complex of differential forms on the orbit space and the basic differential forms on the original manifold. In this paper, this result is general…
Anti-de Sitter space is the Lorentzian space form with negative curvature. In this paper we consider lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space with general codimension. In particular, we investigate the singularities of lightlike hypersurfaces as an application of the theory of Legend…
We give local, explicit representation formulas for n-dimensional spacelike submanifolds which are marginally trapped in the Minkowski space, the de Sitter and anti de Sitter spaces and the Lorentzian products of the sphere and the hyperbolic space by the real line.
In the present paper, we consider the Hodge-de Rham Laplacian that acts on conformal Killing and projective Killing one-forms of a compact Riemannian manifold.
Generalizes integration map to coinvariants of bounded functions.
problem Integration map definition and isomorphism proof for coinvariants.
method Generalizes integration map definition to coinvariants of bounded functions, considering relative bounded de Rham cohomology in presence of boundary.
result Integration map is an isomorphism in top-degree bounded de Rham cohomology.
On any compact manifold of dimension greater than 3, we exhibit a metric whose first positive eigenvalue for the Laplacian acting on p-form is of multiplicity 2. As a corollary, we prescribe the volume and any finite part of the spectrum of the Hodge Laplacian with multiplicity 1 or 2.
On the slit tangent manifold of a Finsler manifold M are given the vertical and the Liouville foliations. In this paper we define some new types of vertical forms with respect to the Liouville foliation on TM^0. We define a cohomology group of TM^0 using these new forms. We prove a de Rham type theorem.