In the joint paper of the author with K. P. Tod [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)] they showed all local solutions of the Einstein-Weyl equations in three dimensions, where the background metric is homogeneous with unimodular isometry group. In particular, they proved that there are no solutions with Nil or Sol as background metric. In this note, these two special cases are presented.
Summary: It is proven that the Poisson algebra of a locally conformal symplectic manifold is integrable by making use of a convenient setting in global analysis. It is also observed that, contrary to the symplectic case, a unified approach to the compact and non-compact case is possible.
Summary: Here, a relation between integrals and variational multipliers of a system of second-order ordinary differential equations is studied. A simple necessary and sufficient local condition for the existence of a multiplier is given.
In the paper under review, the author presents some results on the basis of the Nash-Gromov theory of isometric immersions and illustrates how the same results and ideas can be extended to other structures.
A flag manifold of a compact semisimple Lie group is defined as a quotient where is the centralizer of a one-parameter subgroup of . Then can be identified with the adjoint orbit of in the Lie algebra of . Two flag manifolds and are equivalent if there exists an automorphism such that (equivalent manifolds need not be -diffeomorphic since is not assumed to be inner). In this article, explicit formulas for decompositions of the isotropy representation for all flag manifolds...