arXiv research

We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics. The starting point of our investigation is the higher dimensional (infinitesimal) version of Bianchi's main four theorems on the theory of deformations of quadrics and Bianchi's treatment of the …

The paper constructs and generalizes Poisson brackets for Jacobi elliptic functions and higher-dimensional systems.

Simplified holonomy map for ruled submanifolds in graded manifolds.

We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in $\mathbb{C}^3$ of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere $\…

Generalizes momentum sections to higher-dimensional gauged sigma models.

Paper introduces a new operator and solves equations on higher-dimensional almost Kähler manifolds.

Unified geometric framework for integrability of conservative and dissipative systems.

Study on higher-dimensional black holes, focusing on retractions and scalar quasibound states.

Uniqueness proven for photon spheres in higher-dimensional spacetimes.

We establish a "low rank property" for Sobolev mappings that pointwise solve a first order nonlinear system of PDEs, whose smooth solutions have the so-called "contact property". As a consequence, Sobolev mappings from an open set of the plane, taking values in the first Heisenberg group and that have almost everywhere…

New system modifies constant scalar curvature Kähler condition with a 'Higgs field'.

The paper studies bifurcations in discrete dynamical systems on manifolds.

The paper connects higher-dimensional mechanics to Lie n-algebroids.

Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among local spectral densities, energy densities, global eigenvalue densities, and tot…

We consider 3-webs, hyper-para-complex structures and integrable Segre structures on manifolds of even dimension and generalise the second heavenly Plebański equation in the context of higher-dimensional hyper-para-complex structures. We also characterise the Segre structures admitting a compatible hyper-para-complex s…

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.

In this paper, we generalize the Hersch-Payne-Schiffer inequality for Steklov eigenvalues to higher dimensional case by extending the trick used by Hersch, Payne and Schiffer to higher dimensional manifolds.

A novel method visualizes higher-dimensional spaces using hyperbolic geometry.

The (abelian bosonic) heterotic string effective action, equations of motion and Bianchi identity at order alpha prime in ten dimensions, are shown to be equivalent to a higher dimensional action, its derived equations of motion and Bianchi identity. The two actions are the same up to the gauge fields: the latter are a…

Principal binets generalize curvature line surfaces to square lattices and are a discrete integrable system.

New geometric approach realizes 5D bulk theories with 4D edge modes.

The paper constructs new non-trivial harmonic maps into higher-dimensional target manifolds.

In this short note, we investigate some features of the space $\Inject{d}{m}$ of linear injective maps from $\bbR^d$ into $\bbR^m$; in particular, we discuss in detail its relationship with the Stiefel manifold $V_{m,d}$, viewed, in this context, as the set of orthonormal systems of $d$ vectors in $\bbR^m$. Finally, we…

New superintegrable systems derived from Frobenius structures.

We define the transgression functor which associates to a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold.

This paper concerns some stability properties of higher dimensional catenoids in $\rr^{n+1}$ with $n\ge 3$. We prove that higher dimensional catenoids have index one. We use $δ$-stablity for minimal hypersurfaces and show that the catenoid is $\frac 2n$-stable and a complete $\frac 2n$-stable minimal hypersurface is a …

We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL(2;C)-representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We al…

Researchers find explicit Bäcklund transforms for specific quadrics.

Higher dimensional generalizations of Schwarz's $P$-surface, Schwarz's $D$-surface and Scherk's second surface are constructed as complete embedded periodic minimal hy- persurfaces in $\mathbb R^n$.

Transformed quadrics from 2D to higher dimensions.

We introduce the foliated anti-self dual equation for higher dimensional smooth manifolds with codimension-4 Riemannian foliations. Several fundamental results are established, towards the defining of a Donaldson type invariant for such foliations.

Higher-dimensional contact manifolds lack certain properties.

Geometric models for Lie--Hamilton systems on \(\mathbb{R}^2\) are described.

We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the membrane case.

In this paper we derive necessary and sufficient conditions for a smooth surface in Rn+1 to admit a local 1-quasiconformal parameterization by a domain in Rn (n >= 3). We then apply these conditions to specific hypersurfaces such as cylinders, paraboloids, and ellipsoids. As a consequence, we show that the classical Li…

Constructs Gabor frames for curved manifolds to detect boundaries.

The paper connects geodesic flows and higher-dimensional Reidemeister torsion for hyperbolic orbifolds.

The classical Cohn-Vossen theorem states that two isometric compact convex surfaces in $\mathbb{R}^{3}$ are congruent. In this short note, we generalize the classical Cohn-Vossen Theorem to higher dimensional surfaces in space form $N^{n+1}(K)$ for $n\ge 2$.

The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its non-linear cohomology.

Multisections generalize Heegaard splittings and trisections to higher dimensions.

We analyze higher-dimensional sliding puzzles, finding solvability patterns.

This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic n-space for n greater than 3. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of the hyperbolic 3-space.

The paper proves the existence of infinitely many minimal hypersurfaces in higher-dimensional manifolds.

An iterated function system $Φ$ consisting of contractive similarity mappings has a unique attractor $F \subseteq \mathbb{R}^d$ which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling $\mathcal{T}$ of the con…

The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Ou…

The paper characterizes Eguchi-Hanson space and its higher-dimensional analogs using Lichnerowicz Laplacian.

Computational techniques calculate dimensions of complex structures.

Study shows bounded cohomology vanishes for higher dimensional sphere diffeomorphisms.