The central «pseudopotentials» yielding, in relativistic mechanics, closed (bounded) orbits for any given energy are derived by inspection (of the algebraic form of the hamiltonian).
We generalize brownian motion on a riemannian manifold to the case of a family of metrics which depends on time. Such questions are natural for equations like the heat equation with respect to time dependent laplacians (inhomogeneous diffusions). In this paper we are in particular interested in the Ricci flow which provides an intrinsic family of time dependent metrics. We give a notion of parallel transport along this brownian motion, and establish a generalization of the Dohrn–Guerra or damped...
Summary: In order to get a mathematical understanding of the BRS-transformation and the Slavnov-Taylor identities, we treat them in a finite dimensional setting. We show that in this setting the BRS-transformation is a vector field on a certain supermanifold. The connection to the BRS-complex will be established. Finally we treat the generating functional and the Slavnov-Taylor identity in this setting.
Let be a bounded domain in with smooth boundary . We consider the equation , under zero Neumann boundary conditions, where is open, smooth and bounded and is a small positive parameter. We assume that there is a -dimensional closed, embedded minimal submanifold of , which is non-degenerate, and certain weighted average of sectional curvatures of is positive along . Then we prove the existence of a sequence and a positive solution such that in the sense of measures, where ...
Recentemente, B.-Y. Chen ha introdotto una nuova serie di invarianti riemanniani per ogni varietà riemanniana. Ha anche ottenuto disuguaglianze strette per questi invarianti per sottovarietà di forme spaziali reali e complesse in funzione della loro curvatura media. Nel presente lavoro proviamo analoghe stime per gli invarianti per sottovarietà -totalmente reali e di contatto di una forma spaziale di Sasaki .