Related papers: Quantum geodesic flows and curvature
We determine the explicit quantum ordering for a special class of quantum geodesic functions corresponding to geodesics joining exactly two orbifold points or holes on a non-compact Riemann surface. We discuss some special cases in which…
In this work, the Thermodynamic Geometry (TG) of quantum fluids (QF) is analyzed. We present results for two models. The first one is a quantum hard-sphere fluid (QHS) whose Helmholtz free energy is obtained from Path Integrals Monte Carlo…
Discrete forms of the scalar, sectional and Ricci curvatures are constructed on simplicial piecewise flat triangulations of smooth manifolds, depending directly on the simplicial structure and a choice of dual tessellation. This is done by…
By applying the theory of group-invariant solutions we investigate the symmetries of Ricci flow and hyperbolic geometric flow both on Riemann surfaces. The warped products on $\mathcal {S}^{n+1}$ of both flows are also studied.
We study the geodesic flow of geometrically finite quotients $\Omega/{\Gamma}$ of Hilbert geometries, in particular its recurrence properties. We prove that, under a geometrical assumption on the cusps, the geodesic flow is uniformly…
Suppose we are given a compact Riemannian manifold (Q,g)with completely integrable geodesic flow. Let G be a compact connected Lie group acting freely on Q by isometries. The natural question arises: will the geodesic flow on Q/G equipped…
Statistical mechanics provides an elegant explanation to the appearance of coherent structures in two-dimensional inviscid turbulence: while the fine-grained vorticity field, described by the Euler equation, becomes more and more filamented…
We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to…
The fact that the modular template coincides with the Lorenz template, discovered by Ghys, implies modular knots have very peculiar properties. We obtain a generalization of these results to other Hecke triangle groups. In this context, the…
We continue our investigation of the interplay between causal structures on symmetric spaces and geometric aspects of Algebraic Quantum Field Theory. We adopt the perspective that the geometric implementation of the modular group is given…
The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy momentum tensor in Universes with non trivial topology. The purpose of this work is to…
We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on $\mathbb{R}^{n+1}$ that are noncollapsed at infinity, without assuming bounded…
We describe all local Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral cubic in momenta. We also show that some of these metrics can be extended to the 2-sphere.…
We show how solutions to the Ricci flow on Lorentzian manifolds, along with its generalizations, can be linked to Einstein's field equations. The approach involves deformations of the matter sector that are generated by quadratic…
In this paper, we prove a pseudolocality-type theorem for $\mathcal L$-complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In…
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by…
We consider a geometric flow introduced by Gigli and Mantegazza which, in the case of smooth compact manifolds with smooth metrics, is tangen- tial to the Ricci flow almost-everywhere along geodesics. To study spaces with geometric…
We continue the investigation of general geometric flows of $G_2$-structures initiated by the third author in "Flows of $G_2$-structures, I." Specifically, we determine the possible geometric flows (up to lower order terms) of…
The trajectories of a qubit dynamics over the two-sphere are shown to be geodesics of certain Riemannian or physically-sound Lorentzian manifolds, both in the non-dissipative and dissipative formalisms, when using action-angle variables.…
We start by constructing a Hilbert manifold T of orientation preserving diffeomorphisms of the circle (modulo the group of bi-holomorphic self-mappings of the disc). This space, which could be thought of as a completion of the universal…