We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the holonomy algebra of the normal conformal Cartan connection of a bi-invariant metric. As an example, we apply this calculus to the group SO(4). Its conformal ...

*Correspondence: [email protected] 1Faculty of Applied Sciences, University ‘Politehnica’ of Bucharest, Splaiul Independenţei, No. 313, Bucharest, 060042, Romania Full list of author information is available at the end of the article Abstract In this paper, a new class of generalized of nonconvex multitime multiobjective variational problems is considered. We prove the sufficient optimality...

We evaluate different properties of baryons with a heavy c or b quark. The use of Heavy Quark Symmetry (HQS) provides with an important simplification of the non relativistic three body problem which can be solved by means of a simple variational approach. This scheme is able to reproduce previous results obtained with more involved Faddeev calculations. The resulting wave functions are paramet...

1 Abbreviations and Notations 2

In this note, we use a result of Osserman and Schiffer [?] to give a variational characterization of the catenoid. Namely, we show that subsets of the catenoid minimize area within a geometrically natural class of minimal annuli. To the best of our knowledge, this fact has gone unremarked upon in the literature. As an application of the techniques, we give a sharp condition on the lengths of a ...

We solve resonance problems with respect to the Fuč́ık spectrum of the p-Laplacian using variational methods.

The exterior differential forms are introduced to solve the complicated variational problems on 2-dimensional manifolds in R3. It is easy to generalize this method to the higher dimensional manifolds. [email protected] [email protected]