Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem for the natural diagonal (almost) para-K\"ahlerian structures on the total spaces of the cotangent bundle.Comment: 10 pages, will appear in Czechoslovak Mathematical Journa

Superconformal N=2, D=5 matter with and without actions

We investigate N=2, D=5 supersymmetry and matter-coupled supergravity theories in a superconformal context. In a first stage we do not require the existence of a Lagrangian. Under this assumption, we already find at the level of rigid supersymmetry, i.e. before coupling to conformal supergravity, more general matter couplings than have been considered in the literature. For instance, we construct new vector-tensor multiplet couplings, theories with an odd number of tensor multiplets, and hypermultiplets whose scalar manifold geometry is not hyperkaehler. Next, we construct rigid superconformal Lagrangians. This requires some extra ingredients that are not available for all dynamical systems. However, for the generalizations with tensor multiplets mentioned above, we find corresponding new actions and scalar potentials. Finally, we extend the supersymmetry to local superconformal symmetry, making use of the Weyl multiplet. Throughout the paper, we will indicate the various geometrical concepts that arise, and as an application we compute the non-vanishing components of the Ricci tensor of hypercomplex group manifolds. Our results can be used as a starting point to obtain more general matter-couplings to Poincare supergravity.Comment: 67 pages; v2: title of reference changed and small editing corrections; v3: small typing errors corrected, version published in JHEP; v4: typos corrected; v5: additional term in (2.109) and (4.11); v6: change of order of indices in (2.89

Librations with Mass Transfer in the Sun-Jupiter System

Trojan-type motion is analytically and numerically studied under mass transfer between the primaries with conservation of their total orbital angular momentum. We prove theoretically and numerically our new result that angular libration widths change as m^1/4, (m - Jupiter mass) if they are throughout smaller than about 60 arcd. Numerical examples show that for initial libration widths larger than about 60 arcd, the Trojan is ultimately driven out of the libration domain, becoming an ordinary asteroid, if Jupiter's transferred mass increases by a factor less than about two. Certain processes occurring in our solar system and in extrasolar planetary systems lead to a decrease of the Trojan's libration amplitude, while other processes lead to an increase, respectively