Related papers: Isotropic tori in $\mathbb{C}^m$ revisited

A quasitoric manifold $M$ is a $2n$-dimensional manifold which admits an action of an $n$-dimensional torus which has some nice properties. We determine the isomorphism type of a maximal compact connected Lie-subgroup $G$ of…

Using discretized orthogonal systems (curvature line systems) with periodicity, created using Darboux transformations and their permutability, we have discrete and semi-discrete k-dimensional isothermic tori which are full in n-dimensional…

In every Engel manifold we construct an infinite family of pairwise non-isotopic transverse tori that are all smoothly isotopic. To distinguish the transverse tori in the family we introduce a homological invariant of transverse tori that…

We construct monotone Lagrangian tori in the standard symplectic vector space, in the complex projective space and in products of spheres. We explain how to classify these Lagrangian tori up to symplectomorphism and Hamiltonian isotopy, and…

We present an example of two isotopic but not strongly isotopic commutative semifields. This example shows that a recent result of Coulter and Henderson on semifield of order p^n, n odd, can not be generalized to the case n even.

We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.

We give a proof of the convergence of an algorithm for the construction of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. The existence of such invariant tori is proved by leading the Hamiltonian to a suitable…

The purpose of this note is to present a construction of an infinite family of symplectic tori T_{p} representing an arbitrary multiple of the homology class of the fiber of an elliptic surface E(n), for n > 2, such that, for i \neq j,…

We show that the space of Lagrangians which are Hamiltonian isotopic to the Clifford torus in a complex projective space or in the four-dimensional quadric, taken with Chekanov's Lagrangian Hofer metric, contains a quasi-isometric copy of…

We prove a version of the Thom Isotopy Theorem for nonproper semialgebraic maps $f\colon X\rightarrow \mathbb{R}^m$, where $X \subset\mathbb{R}^n$ is a semialgebraic set and $f$ is the restriction to $X$ of a smooth semialgebraic map…

For any pair of integers $n\geq 1$ and $q\geq 2$, we construct an infinite family of mutually non-isotopic symplectic tori representing the homology class $q[F]$ of an elliptic surface E(n), where $[F]$ is the homology class of the fiber.…

Answering a question of A. Rapinchuk, we construct examples of non- isomorphic semisimple algebraic groups H1 and H2 of type G2 with coherently equivalent systems of maximal k-tori.

In this paper we construct $n$-valued maps on $k$-dimensional tori, where $n,k\geq 2$, that are not homotopic to affine $n$-valued maps. This is in high contrast with the single valued case, where any such map is homotopic to an affine…

We consider proper-biharmonic flat tori with constant mean curvature (CMC) in spheres and find necessary and sufficient conditions for certain rectangular tori and square tori to admit full CMC proper-biharmonic immersions in…

In the present paper, we prove that two discrete rectangular tori are isospectral if and only if they are isomorphic.

We construct examples of $C^\infty$ smooth submanifolds in ${\Bbb C}^n$ and ${\Bbb R}^n$ of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact…

We investigate conditions under which a two-dimensional complex semi-torus splits into a direct product of C^* and a one-dimensional compact complex torus.

All principal orbits of the standard Hamiltonian $T^n$-action on the complex projective space ${\mathbb C}P^n$ are Lagrangian tori.In this article, we prove that most of them are not volume minimizing under Hamiltonian isotopies of…

We generalize to some PDEs a theorem by Nekhoroshev on the persistence of invariant tori in Hamiltonian systems with $r$ integrals of motion and $n$ degrees of freedom, $r\leq n$. The result we get ensures the persistence of an…

We consider four-dimensional homogeneous pseudo-Riemannian manifolds with non-trivial isotropy and completely classify the cases giving rise to non-trivial homogeneous Ricci solitons. In particular, we show the existence of non-compact…