We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the 1 : 6 : 1 integrable case quartic potential. A generalisation of the 1 : 6 : 8 case is sim...

In this paper we relate the Fefferman–Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of the usual normalisation condition, one can construct the conformal standard tractor bundle and the normal standard tractor connection, which are equivalent to...

The equivalence problem for CR structures can be viewed as a special case of the equivalence problem for G-structure. This paper uses Cartan’s methods (in modernized form) to show that a CR manifold of codimension 3 or greater with suitably generic Levi form admits a canonical connection on a reduced structure bundle whose group is isomorphic to the multiplicative group of complex numbers. As c...

In this article we are going to provide a brief survey of results on Serre’s conjectures on intersection multiplicities, Hochster’s canonical element conjecture and a connection between these two sets of conjectures as well. In particular we will formulate a new connection between canonical element conjecture and a special case of a question involving intersection multiplicity and χ2-property o...

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces ...

the famous primary and cyclic decomposition theorems along with the tightly related rational and jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.

Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonlinear connection associated with a given regular connection, in the pullback bundle, ...

The aim of the present paper is to provide an intrinsic investigation of the fundamental properties of the most important geometric objects associated with the fundamental linear connections on a Finsler manifold. We introduce and investigate intrinsically the most general properties concerning the torsion tensor fields and the curvature tensor fields associated with a certain regular connectio...

The aim of this research work is to define and characterize a new class of n-ary multialgebra that may be called canonical (m, n)&minus hypermodules. These are a generalization of canonical n-ary hypergroups, that is a generalization of hypermodules in the sense of canonical and a subclasses of (m, n)&minusary hypermodules. In addition, three isomorphism theorems of module theory and canonical ...