相关论文: The Geometric Origin of the Cayley-Hamilton Theore…

We apply the Atiyah-Singer index theorem and tensor products of elliptic complexes to the cohomology of transitive Lie algebroids. We prove that the Euler characteristic of a representation of a transitive Lie algebroid $A$ over a compact…

We construct a bi-Hamiltonian structure for the holomorphic spin Sutherland hierarchy based on collective spin variables. The construction relies on Poisson reduction of a bi-Hamiltonian structure on the holomorphic cotangent bundle of…

Low-dimensional descriptions of large systems of coupled oscillators and spiking neurons rely heavily on the Lorentzian Ansatz. We show that its privileged role is geometric rather than heuristic: for the transport induced by Riccati…

The Hamiltonian approach to isomonodromic deformation systems for generic rational covariant derivative operators on the Riemann sphere, having any matrix dimension $r$ and any number of isolated singularities of arbitrary Poincar\'e rank,…

A classical result due to Levinson characterizes the existence of non-zero functions defined on a circle vanishing on an open subset of the circle in terms of the pointwise decay of their Fourier coefficients [13]. We prove certain analogue…

Caianiello's derivation of Quantum Geometry through an isometric embedding of the spacetime ({\bf M},\tilde{g}) in the pseudo-Riemannian structure ({\bf T^*M},g^*_{AB}) is reconsidered. In the new derivation, a non-linear connection and the…

We present a general construction of hypersurfaces with vanishing hessian, starting from any irreducible non-degenerate variety whose dual variety is a hypersurface and based on the so called Dual Cayley Trick. The geometrical properties of…

We extend the Kontsevich formality $L_\infty$-morphism $\U\colon T^\ndot_\poly(\R^d)\to\D^\ndot_\poly(\R^d)$ to an $L_\infty$-morphism of an $L_\infty$-modules over $T^\ndot_\poly(\R^d)$, $\hat \U\colon C_\ndot(A,A)\to\Omega^\ndot(\R^d)$,…

In the present paper we prove that every k-dimensional Cartesian product of Kingman convolutions can be embedded into a k-dimensional symmetric convolution (k=1, 2, ...) and obtain an analogue of the Cram\'er-L\'evy theorem for…

Five years ago, Lane Hughston showed that some of the symmetric informationally complete positive operator valued measures (SICs) in dimension 3 coincide with the Hesse configuration (a structure well known to algebraic geometers, which…

In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved.…

We prove the Hardy-Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample,…

In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…

The Simon tensor gives rise to a local characterization of the Kerr-NUT family in the stationary class of vacuum spacetimes. We find that a symmetric and traceless tensor in the quotient space of the stationary Killing trajectory offers a…

The prototype of mutually independent systems are systems which are localized in spacelike separated regions. In the framework of locally covariant quantum field theory we show that the commutativity of observables in spacelike separated…

According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure vanishes at the point. Similar splitting results…

We use the computer algebra system \textit{GRTensorII} to examine invariants polynomial in the Riemann tensor for class $B$ warped product spacetimes - those which can be decomposed into the coupled product of two 2-dimensional spaces, one…

We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual…

In this paper, we study the geometric configurations of a finite set of points having the Cayley-Bacharach property in the $n$-dimensional projective space $\bbP^n$. Our main contribution is the proof of the Levinson-Ullery conjecture for…

Classical variational Hodge structure theory characterizes the algebraicity of Hodge classes by studying the transversality of period mappings under geometric deformations. However, when algebraic varieties lack appropriate deformation…