Of the structure of the Euler mapping
On -tensor fields on symplectic manifolds
Two symplectic structures on a manifold determine a (1,1)-tensor field on . In this paper we study some properties of this field. Conversely, if is (1,1)-tensor field on a symplectic manifold then using the natural lift theory we find conditions under which , is symplectic.
On 3-dimensional CR-manifolds
On 3-dimensional Lie algebras of vector fields
On a class of exact locally conformal cosymplectic manifolds.
On a class of variational problems defined by polynomial Lagrangians
On a connection with torsion zero
On a coregular division of a differential space by an equivalence relation
On a generalization of Helmholtz conditions
Helmholtz conditions in the calculus of variations are necessary and sufficient conditions for a system of differential equations to be variational ‘as it stands’. It is known that this property geometrically means that the dynamical form representing the equations can be completed to a closed form. We study an analogous property for differential forms of degree 3, so-called Helmholtz-type forms in mechanics (), and obtain a generalization of Helmholtz conditions to this case.
On a horizontal structure on differentiable manifolds
On a multiplicativity up to homotopy of the Gugenheim map.
On a new normalization for tractor covariant derivatives
A regular normal parabolic geometry of type on a manifold gives rise to sequences of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative on the corresponding tractor bundle , where is the normal Cartan connection. The first operator in the sequence is overdetermined and it is well known that yields the prolongation of this operator in the homogeneous case . Our first main result...
On a Pair of Connections on a Principal Fibre Bundle
On a solvability condition for systems with an injective symbol in terms of iterations of double layer potentials.
On a weak coregular division of a differential space
On algebraic solutions of algebraic Pfaff equations
We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.
On Algebraicity of Global Real Analytic Sets and Functions
On an integral formula
On approximating submanifolds by algebraic sets and a solution to the Nash conjecture.
On bilinear structures on differentiable manifolds