Let H be the hyperbolic space of dimension n + 1. A geodesic foliation of H is given by a smooth unit vector field on L all of whose integral curves are geodesics. Each geodesic foliation of L determines an n-dimensional ...

We obtain some Hermite-Hadamard type inequalities for convex functions in a global non-positive curvature space.

Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical ...

Let A be a von Neumann algebra and PA the manifold of projections in A. There is a natural linear connection in PA, which in the finite dimensional case coincides with the the Levi-Civita connection of the Grassmann manifold ...

We study the existence and stability of circular geodesics in a family of asymptotically AdS static black holes in New Massive Gravity theory. We show that the mathematical sign of the hair parameter determines the existence ...

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical ...

Let M be a type II_1 von Neumann algebra,  τ a trace in M, and l^2 (M,τ) the GNS Hilbert space of τ. We regard the unitary group U_M as a subset of l^2 (M,τ), and characterize the shortest smooth curves of unitaries joining ...