相关论文: Self-dual Harmonicity: the planar case
We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold M to a two-dimensional conformal manifold N can be, locally, `extended' to a unique harmonic morphism from the heaven…
We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties $X$ and $Y$ in dual projective spaces are…
For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such systems dual if the corresponding ruled surfaces are dual. We…
We consider compact oriented four-manifolds with harmonic self-dual Weyl curvature in addition to a pinching condition.
We present a necessary and sufficient condition for the topological equivalence of a continuous function on a plane to a projection onto one of coordinates.
Mechanism of the Fano resonances in planar metamaterials demonstrate based on the coupled two-oscillator model. We have described the optical spectrums like reflectance and transmittance near the resonances of bright mode (continuum mode)…
We discuss solutions of several questions concerning the geometry of conformal planes.
This article describes our invention of a new poetic form based on projective geometry. In doing this we also explore the 'what ifs' in mathematics and poetry which spark the creative processes of poet and mathematician. In other words,…
Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an…
We briefly review the structure and properties of self-dual field actions.
We provide examples of foliations on the complex projective plane $\CP^2$ carrying positive foliated harmonic currents whose supports coincide with singular Levi-flats which, in turn, can be chosen real-analytic (but non-algebraic) or…
The present paper is dedicated to illustrating an extension of polar duality between Fano toric varieties to a more general duality, called \emph{framed} duality, so giving rise to a powerful and unified method of producing mirror partners…
In this paper we extend the discussion on Homological Mirror Symmetry for Fano toric varieties presented by Hori and Vafa to more general case of monotone symplectic manifolds with real polarizations. We claim that the Hori -- Vafa…
We classify Fano fivefolds of index two which are projectivization of rank two vector bundles over four dimensional manifolds.
We give some rationality constructions for Fano threefolds with canonical Gorenstein singularities.
It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity…
We completely describe the Fano scheme of lines for a projective toric surface in terms of the geometry of the corresponding lattice polygon.
We study a generalization of the concept of harmonic conjugation from projective geometry and full algebraic matroids to a larger class of matroids called \emph{harmonic matroids}. We use harmonic conjugation to construct a projective plane…
We investigate a double cavity optomechanical system(OMS) generating single and double Fano resonance(multi Fano). By altering a single parameter, the tunneling rate $g$ of the middle mirror, we are able to switch between single and double…
The purpose of this paper is to present projective geometry in a synthetic, visual and intuitive style through the central notion of harmonicity which leads to harmonic curves. This presentation includes new results, unpublished proofs of…