The superposition operator in Musielak-Orlicz spaces of vector-valued functions
The symbol of a function of a pseudo-differential operator
We give an explicit formula for the symbol of a function of an operator. Given a pseudo-differential operator on with symbol and a smooth function , we obtain the symbol of in terms of . As an application, Bohr-Sommerfeld quantization rules are explicitly calculated at order 4 in .
The symmetric tensor Lichnerowicz algebra and a novel associative Fourier-Jacobi algebra.
The symmetry algebra and conserved Currents for Klein-Gordon equation on quantum Minkowski space
The symmetry operators for Klein-Gordon equation on quantum Minkowski space are derived and their algebra is studied. The explicit form of the Leibniz rules for derivatives and variables for the case Z=0 is given. It is applied then with symmetry operators to the construction of the conservation law and the explicit form of conserved currents for Klein-Gordon equation.
The symplectic geometry of affine connenctions on surfaces.
The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics
The symplectic Thom conjecture.
The systolic constant of orientable Bieberbach 3-manifolds
A compact manifold is called Bieberbach if it carries a flat Riemannian metric. Bieberbach manifolds are aspherical, therefore the supremum of their systolic ratio, over the set of Riemannian metrics, is finite by a fundamental result of M. Gromov. We study the optimal systolic ratio of compact -dimensional orientable Bieberbach manifolds which are not tori, and prove that it cannot be realized by a flat metric. We also highlight a metric that we construct on one type of such manifolds () which...
The Tanaka-Webster connection for almost -manifolds and Cartan geometry
We prove that a CR-integrable almost -manifold admits a canonical linear connection, which is a natural generalization of the Tanaka–Webster connection of a pseudo-hermitian structure on a strongly pseudoconvex CR manifold of hypersurface type. Hence a CR-integrable almost -structure on a manifold is canonically interpreted as a reductive Cartan geometry, which is torsion free if and only if the almost -structure is normal. Contrary to the CR-codimension one case, we exhibit examples of non normal...
The tangent bundle of an almost-complex free loopspace.
The tangent bundle of -velocities over a homogeneous space
The Tangent cone of an Aleksandrov space of curvature.
The theorem of desargues in planes with analogues to Euclidian angular bisectors.
The Theory of differential invariance and infinite dimensional Hamiltonian evolutions
In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.
The theory of differential invariants and KDV hamiltonian evolutions
The theory of Kaluza-Klein-Jordan-Thiry revisited
The third Betti number of a positively pinched riemannian six manifold
We prove that if the sectional curvature, , of a compact 6-manifold without boundary satisfies then its third (real) Betti number is zero.
The Tightness of Extrinsic Symmetric Submanifolds.
The tightness of tubes.
The topology of large -surfaces bounded by a convex curve