Related papers: Real hypersurfaces in complex hyperbolic two-plane…

We consider the Jacobi operator (T,D(T)) associated with an indeterminate Hamburger moment problem, i.e., the operator in $\ell^2$ defined as the closure of the Jacobi matrix acting on the subspace of complex sequences with only finitely…

In this paper, we provide conceptional explanations for the geodesic and Jacobi field correspondences for homothetic navigation, and then let them guide us to the shortcuts to some well known flag curvature and S-curvature formulas. They…

We discuss several new bi-Hamiltonian integrable systems on the plane with integrals of motion of third, fourth and sixth order in momenta. The corresponding variables of separation, separated relations, compatible Poisson brackets and…

In this paper, we investigate the complex symmetric structure of generalized weighted composition operators $D_{m,\psi,\varphi}$ on the weighted Hardy space $H^2(\beta)$. We obtain explicit conditions for $ D_{m,\psi,\varphi}$ to be complex…

We use precise asymptotic expansions for Jacobi functions $\phi^{(\alpha,\beta)}_\lambda$ parameters $\alpha$, $\beta$ satisfying $\alpha>1/2$, $\alpha>\beta>-1/2$, to generalizing classical H\"ormander-type multiplier theorem for the…

Motivated by Buchstaber's and Terzic' work on the complex Grassmannians G(2,4) and G(2,5) we describe the moment map and the orbit space of oriented Grassmannians of planes under the action of a maximal compact torus. Our main tool is the…

In this paper we obtain two types of optimal inequalities consisting of the normalized scalar curvature and the generalized normalized $\delta$-Casorati curvatures for real hypersurfaces of complex two-plane Grassmannians and complex…

Let (M,g) be a Riemannian manifold and G a nondegenerate g-natural metric on its tangent bundle T M . In this paper we establish a relation between the Jacobi operators of (M,g) and that of (T M,G). In the case of a Riemannian surface…

An element [\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\phi} for C(x). The Pl\"ucker coordinates…

A sequence of combinatorial mutations of matching field polytopes preserves the property of giving rise to a toric degeneration of Grassmannians. In this paper, we find a way to check that two matching field polytopes are combinatorial…

We rewrite various lattice Hamiltonian in condensed matter physics in terms of U(2/2) operators that we introduce. In this representation the symmetry structure of the models becomes clear. Especially, the Heisenberg, the supersymmetric t-J…

For a symmetric pair $(G,H)$ of reductive groups we construct a family of intertwining operators between spherical principal series representations of $G$ and $H$ that are induced from parabolic subgroups satisfying certain compatibility…

We prove that the (homotopy) hypercommutative algebra structure on the de Rham cohomology of a Poisson or Jacobi manifold defined by several authors is (homotopically) trivial, i.e. it reduces to the underlying (homotopy) commutative…

In this paper we analyze two different functional formulations of classical mechanics. In the first one the Jacobi fields are represented by bosonic variables and belong to the vector (or its dual) representation of the symplectic group. In…

This is a slightly revised version of the author's 2010 diploma thesis. It is concerned with the interplay between real multiplication on Jacobian varieties, as the title suggests, and complex geodesics in the moduli space of curves. Large…

We characterize the spectrum of one-dimensional Jacobi operators H=aS^{+}+a^{-}S^{-}+b in l^{2}(\Z) with quasi-periodic complex-valued algebro-geometric coefficients (which satisfy one (and hence infinitely many) equation(s) of the…

We show that Jacobi fields along harmonic maps between suitable spaces preserve conformality, holomorphicity, real isotropy and complex isotropy to first order; this last being one of the key tools in the proof by Lemaire and the author of…

We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well known gap in the spectrum of the Laplacian on the upper half-plane with hyperbolic metric. We make some…

It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such…

In this paper, we investigate the normal weighed composition operators $W_{\psi,\varphi}$ which is $\mathcal{J}-$symmetric, $\mathcal{C}_1-$symmetric and $\mathcal{C}_2-$symmetric on the Hardy space $H^2(\mathbb{D})$ respectively. Firstly,…