arXiv research

Normalizes pseudo-Einstein contact forms for easier analysis.

The paper defines normal forms for rational 3-tangles and shows a sequence of moves to transform one form to another.

This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the normal exponential map on the finite boundary. As a main application, a normal fo…

We find a normal form for two-input flat discrete-time systems.

In this article, we first describe a normal form of real-analytic, Levi-nondegenerate submanifolds of $C^N$ of codimension d $\ge$ 1 under the action of formal biholomorphisms, that is, of perturbations of Levi-nondegenerate hyperquadrics. We give a sufficient condition on the formal normal form that ensures that the n…

This note analyzes the normal form of gradient Ricci 4-solitons.

We introduce the notion of a ribbon-clasp surface-link, which is a generalization of a ribbon surface-link. We generalize the notion of a normal form on embedded surface-links to the case of immersed surface-links and prove that any (immersed) surface-link can be described in a normal form. It is known that an embedded…

Study on immersions with flat normal bundle in curved spaces.

Proves convergence of normal forms for infinite-dimensional Lie pseudo-group actions.

Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm…

In this paper we construct a large class of new normal forms for Levi-nondegenerate real hypersurfaces in complex spaces. We adopt a general approach illustrating why these normal forms are natural and which role is played by the celebrated Chern-Moser normal form. The latter appears in our class as the one with the "m…

The paper characterizes surfaces in 4D space forms with flat normal connection.

Paper classifies rational 3-tangles using normal forms and minimal coordinates.

Rolling two hyperboloid surfaces is described using a Monge normal form.

Formal Normal Form created for special CR singularities.

A 1-bridge torus knot in a 3-manifold of genus $\le 1$ is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal f…

Formal normal form created for real-smooth hypersurfaces.

We introduce in this paper normal twistor equations for differential forms and study their solutions, the so-called normal conformal Killing forms. The twistor equations arise naturally from the canonical normal Cartan connection of conformal geometry. Reductions of its holonomy are related to solutions of the normal t…

Alternative closed-form formula for spread call option prices under log-normal models.

2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.

Researchers create normal forms for CR manifolds in complex space.

A normal form for edge metrics is derived under the necessary conditions that the metric be normalized and exact. The normal forms for such an edge metric are shown to be in 1-1 correspondence with representative metrics for a reduced conformal infinity on the boundary. The normal form is constructed via solution of a …

A differential 1-form $α$ on a manifold of odd dimension $2n+1$, which satisfies the contact condition $α\wedge (dα)^n \neq 0$ almost everywhere, but which vanishes at a point $O$, i.e. $α(O) = 0$, is called a \textit{singular contact form} at $O$. The aim of this paper is to study local normal forms (formal, analytic …

We solve the local equivalence problem for second order (smooth or analytic) ordinary differential equations. We do so by presenting a {\em complete convergent normal form} for this class of ODEs. The normal form is optimal in the sense that it is defined up to the automorphism group of the model (flat) ODE $y"=0$. For…

Local normal forms for symmetrical contact structures on 3-manifolds.

We construct a formal normal form for a real 2-codimensional submanifold $M\subset\mathbb{C}^{N+1}$ near a CR singularity approximating the sphere. This result gives a higher dimensional extension of Huang-Yin's normal form in $\mathbb{C}^{2}$.

Normal forms for Q-structures on graded manifolds explained.

We give a complete list of normal forms for the 2-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.

The paper normalizes Poisson saturation of coregular submanifolds.

We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the Chern-Moser normalization into pure intrinsic setting, whereas the other directly extends the (extrinsic) Chern-Moser normal form by allowing non-C…

Complete normal forms for specific real hypersurfaces in complex space are constructed.

The study examines stability of triharmonic hypersurfaces in space forms.

Theory of symplectic reduction in infinite dimensions developed.

It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.

In this paper, by studying the position of umbilical normal vectors in the normal bundle, we prove that pseudo-umbilical totally real submanifolds with flat normal connection in non-flat complex space forms must be minimal.

The study classifies and normalizes 3D gl-regular Nijenhuis operators.

We construct a complete convergent normal form for a real hypersurface in $\CC{N},\,N\geq 2$ at generic Levi degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. In particular, we obtain, in the spirit of the work of Chern and Moser \cite{chern}, distinguished curves in the …

We consider free and proper cotangent-lifted symmetries of Hamiltonian systems. For the special case of G = SO(3), we construct symplectic slice coordinates around an arbitrary point. We thus obtain a parametrisation of the phase space suitable for the study of dynamics near relative equilibria, in particular for the B…

Normal forms for equivariant maps in infinite dimensions established.

Method studies equivalence of second order ODEs under specific transformations.

Normal forms and invariants for nondegenerate hypersurfaces in C^2.

A local normal form theorem for smooth equivariant maps between Fréchet manifolds is established. Moreover, an elliptic version of this theorem is obtained. The proof these normal form results is inspired by the Lyapunov-Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces, and uses a s…

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized $δ$-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent …

The paper studies special surfaces in 4D space forms with specific geometric properties.

The study shows that the second fundamental form is intrinsic under certain conditions in space forms.

We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is conformally flat. In either case, the vector field is locally conjugate to a no…

Normal forms prove dynamical results for magnetic fields on surfaces.

In this paper we define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. These are intrinsically related to the Gromov D-operator. As an application we deduce normal forms of 1-jets of almost complex structures along a submanifold.…