Related papers: WDVV Equations

In this paper, we investigate the DDVV-type inequality for Riemannian maps from quaternionic space forms to Riemannian manifolds. We also discuss the equality case of the derived inequality with application.

In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.

We calculate the genus 2 correlation functions of two-dimensional topological gravity, in a background with two primary fields, using the genus 2 topological recursion relations.

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

We show how the WDVV equations and the DZM system can be characterized via a background family of functions.

A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that…

In this work, we consider 2-surfaces in ${\mathbb R}^3$ arising from the modified Korteweg de Vries (mKdV) equation. We give a method for constructing the position vector of the mKdV surface explicitly for a given solution of the mKdV…

We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…

The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…

Using the AKSZ prescription we construct 2D and 3D topological field theories associated to generalized complex manifolds. These models can be thought of as 2D and 3D generalizations of A- and B-models. Within the BV framework we show that…

In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric theories. We discuss…

We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.

We determine a strong form of the decomposition theorem for proper toric maps over finite fields.

The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…

We study weighted transfer operators associated to a piecewise expanding map on a compact manifold, and a piecewise Holder weight, acting on Sobolev spaces. We bound the essential spectral radius in terms of a topological pressure for a…

This paper gives a classification of the topology of vector fields which are nowhere tangent to the fibers of a Seifert fibering.

We consider the behavior of level lines of two-dimensional potentials, which play an important role in the physics of ``two-layer'' systems. Potentials of this type are quasiperiodic and, at the same time, can also be considered as a model…

We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…

After sketching recent advances and subtleties in classical relativistically covariant field theories, we give in this short Note some indications as to how the deformation quantization approach can be used to solve or at least give a…