Remarks on symplectic sectional curvature

Some Remarks on Symplectic Automorphisms

Remarks on Dispersive Estimates and Curvature

We investigate connections between certain dispersive estimates of a (pseudo)differential operator of real principal type and the number of nonvanishing curvatures of its characteristic manifold. More precisely, we obtain sharp thresholds for the range of Lebesgue exponents depending on the specific geometry.

A few remarks about symplectic filling

We show that any compact symplectic manifold (W,ω) with boundary embeds as a domain into a closed symplectic manifold, provided that there exists a contact plane ξ on ∂W which is weakly compatible with ω , i.e. the restriction ω|ξ does not vanish and the contact orientation of ∂W and its orientation as the boundary of the symplectic manifold W coincide. This result provides a useful tool for ne...

Structure of the curvature tensor on symplectic spinors

We study symplectic manifolds (M, ω) equipped with a symplectic torsion-free affine (also called Fedosov) connection ∇ and admitting a metaplectic structure. Let S be the so called symplectic spinor bundle and let R be the curvature tensor field of the symplectic spinor covariant derivative ∇ associated to the Fedosov connection ∇. It is known that the space of symplectic spinor valued exterior...

Homogeneous symplectic manifolds with Ricci - type curvature

We consider invariant symplectic connections ∇ on homogeneous symplectic manifolds (M, ω) with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an integrable almost complex structure on the bundle of almost complex structures compatible with the symplectic structure. If M is compact with finite fundamental group then (M...