Related papers: Calabi product Lagrangian immersions in complex pr…
The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian (potential) coordinates and symmetries and conservation…
Let $M$ be a complex $n$-dimensional projective manifold in $\mathbb{P}^{n+r}$ endowed with the Fubini-Study metric of constant holomorphic sectional curvature $1$, $\sigma$ its second fundamental form, and $\underline{|\sigma|}^2$ the mean…
We study real Lagrangian analytic surfaces in C^2 with a non-degenerate complex tangent. Webster proved that all such surfaces can be transformed into a quadratic surface by formal symplectic transformations of C^2. We show that there is a…
In this paper, we introduce Clairaut warped product Riemannian maps. To study these kind of maps, first, we find the condition of geodesic of a regular curve. Then we obtain the conditions for a warped product Riemannian map to be Clairaut…
The grassmannian of hermitian lagrangian spaces in $\mathbb{C}^n\oplus \mathbb{C}^n$ is a natural compactification of the space of hermitian $n\times n$ matrices. We describe a Schubert-like, Whitney regular stratification on this space…
The famous Nash embedding theorem published in 1956 was aiming for the opportunity to use extrinsic help in the study of (intrinsic) Riemannian geometry, if Riemannian manifolds could be regarded as Riemannian submanifolds. However, this…
The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to…
The interplay between the chiral anomaly and the non-leptonic weak Hamiltonian is studied. The structure of the corresponding effective Lagrangian of odd intrinsic parity is established. It is shown that the factorizable contributions…
Minimal surfaces in the Riemannian product of surfaces of constant curvature have been considered recently, particularly as these products arise as spaces of oriented geodesics of 3-dimensional space-forms. This papers considers more…
In this paper, we determine all conformal minimal immersions of 2-spheres in complex Grassmann manifold $G(2,N; \mathbb{C})$ with parallel second fundamental form.
We perform a numerical simulation of Faraday waves forced with two-frequency oscillations using a level-set method with Lagrangian-particle corrections (particle level-set method). After validating the simulation with the linear stability…
Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of…
It is known that all weakly conformal Hamiltonian stationary Lagrangian immersions of tori in the complex projective plane may be constructed by methods from integrable systems theory. This article describes the precise details of a…
By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi functions of the second kind in kernel form. We also derive…
In this work we characterize certain immersed closed hypersurfaces of some ambient manifolds via the second eigenvalue of the Jacobi operator. First, we characterize the Clifford torus as the surface which maximizes the second eigenvalue of…
Motivated by Calabi's calculation of the second variation sign for locally strongly convex affine maximal surfaces in equiaffine geometry, we first prove that every Calabi extremal surface is also maximal in the Calabi affine geometry. By…
We examine the possibility of recovering the supersymmetric (and soft supersymmetry breaking) Lagrangian parameters as direct {\em analytical} expressions of appropriate physical masses, for the unconstrained (but CP and R-parity…
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
The eigenstates of d-dimensional quasicrystalline models with a separable Hamiltonian are studied within the tight-binding model. The approach is based on mathematical sequences, constructed by an inflation rule P = {w -> s, s -> sws^(b-1)}…