Related papers: Jacobi Fields in Optimal Control I: Morse and Masl…

We study asymptotics of generalized eigenvectors associated with Jacobi matrices. Under weak conditions on the coefficients we identify when the matrices are self-adjoint and show that they satisfy strong non-subordinacy condition.

In this lecutre note, we consider infinite dimensional Lie algebras of generalized Jacobi matrices $\mathfrak{g}J(k)$ and $\mathfrak{gl}_\infty(k)$, which are important in soliton theory, and their orthogonal and symplectic subalgebras. In…

In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of Hamiltonian systems in Classical Mechanics, that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure…

In this article, I demonstrate a new method to derive Jacobi metrics from Randers-Finsler metrics by introducing a more generalised approach to Hamiltonian mechanics for such spacetimes and discuss the related applications and properties. I…

We give a detailed path integral derivation of the elliptic genus of a supersymmetric coset conformal field theory, further twisted by a global U(1) symmetry. It gives rise to a Jacobi form in three variables, which is the modular…

The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations of the action corresponding to a Lagrangian defined on a…

In this thesis, we study the deformation problem of coisotropic submanifolds in Jacobi manifolds. In particular we attach two algebraic invariants to any coisotropic submanifold $S$ in a Jacobi manifold, namely the $L_\infty[1]$-algebra and…

A Lie system is a system of differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields, a Vessiot-Guldberg Lie algebra. We define and analyze…

We define Jacobi forms with complex multiplication. Analogous to modular forms with complex multiplication, they are constructed from Hecke characters of the associated imaginary quadratic field. From this construction we obtain a Jacobi…

Let $p$ be a prime, and $q$ a power of $p$. Using Galois theory, we show that over a field $K$ of characteristic zero, the endomorphism algebras of the jacobians of certain superelliptic curves $y^q=f(x)$ are products of cyclotomic fields.

Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete…

Consider the Jacobian of a hyperelliptic genus two curve defined over a prime field of characteristic p and with complex multiplication. In this paper we show that the p-Sylow subgroup of the Jacobian is either trivial or of order p.

Previous work by the authors (this journal, \vol{60} (2008), 1009-1044) produced equations that hold on certain loci of the Jacobian of a cyclic $C_{rs}$ curve. A curve of this type generalizes elliptic curves, and the equations in question…

In this paper, we prove the existence of classical solutions to second boundary value prob- lems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability…

We develop a constructive procedure for arriving at the Hamilton-Jacobi framework for the so-called affine in acceleration theories by analysing the canonical constraint structure. We find two scenarios in dependence of the order of the…

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect…

We study invariants defined by count of charged, elliptic $J$-holomorphic curves in locally conformally symplectic manifolds. We use this to define $\mathbb{Q} $-valued deformation invariants of certain complete Riemann-Finlser manifolds…

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 discuss some properties of Jacobi fields that do not involve assumptions on the curvature endomorphism. We compare indices of different spaces of Jacobi fields and give some applications to Riemannian geometry.

Let $X$ be a regular geometrically integral variety over an imperfect field $K$. Unlike the case of characteristic $0$, $X':=X\times_{\mathrm{Spec}\,K}\mathrm{Spec}\,K'$ may have singular points for a (necessarily inseparable) field…