General poisson algebras
Summary: [For the entire collection see Zbl 0742.00067.]A general theory of fibre bundles structured by an arbitrary differential-geometric category is presented. It is proved that the structured bundles of finite type coincide with the classical associated bundles.
[For the entire collection see Zbl 0699.00032.] A manifold (M,g) is said to be generalized Einstein manifold if the following condition is satisfied where S(X,Y) is the Ricci tensor of (M,g) and (X), (X) are certain -forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g( (X), (X)).
Summary: We provide a geometric interpretation of generalized Jacobi morphisms in the framework of finite order variational sequences. Jacobi morphisms arise classically as an outcome of an invariant decomposition of the second variation of a Lagrangian. Here they are characterized in the context of generalized Lagrangian symmetries in terms of variational Lie derivatives of generalized Euler-Lagrange morphisms. We introduce the variational vertical derivative and stress its link with the classical...
Summary: Geodesics and curvature of semidirect product groups with right invariant metrics are determined. In the special case of an isometric semidirect product, the curvature is shown to be the sum of the curvature of the two groups. A series of examples, like the magnetic extension of a group, are then considered.
[For the entire collection see Zbl 0742.00067.]Let be a connected semisimple Lie group with finite center. In this review article the author describes first the geometric realization of the discrete series representations of on Dolbeault cohomology spaces and the tempered series of representations of on partial Dolbeault cohomology spaces. Then he discusses his joint work with Wilfried Schmid on the construction of maximal globalizations of standard Zuckerman modules via geometric quantization....
We review and discuss a method to normalize triangles by the longest-edge. A geometric diagram is described as a helpful tool for studying and interpreting the quality of triangle shapes during iterative mesh refinements. Modern CAE systems as those implementing the finite element method (FEM) require such tools for guiding the user about the quality of generated triangulations. In this paper we show that a similar method and corresponding geometric diagram in the three-dimensional case do not exist....