Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems.
Generalized Einstein manifolds
[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)).
Generalized Hantzsche-Wendt flat manifolds.
We study the family of closed Riemannian n-manifolds with holonomy group isomorphic to Z2n-1, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structure, compute some invariants, and find relations between them, illustrated in a graph connecting the family.
Generalized Hasimoto transform of one-dimensional dispersive flows into compact Riemann surfaces.
Generalized Hopf manifolds with flat local Kaelher metrics
Generalized inverses of elliptic systems of differential operators with constant coeffcients and related Reduce programs for explicit calculations
Generalized Jacobi morphisms in variational sequences
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...
Generalized Kählerian manifolds and transformation of generalized contact structures
The aim of this paper is two-fold. First, new generalized Kähler manifolds are constructed starting from both classical almost contact metric and almost Kählerian manifolds. Second, the transformation construction on classical Riemannian manifolds is extended to the generalized geometry setting.
Generalized Lie bialgebroids and strong Jacobi-Nijenhuis structures.
Generalized Miron's -connection in the recurrent -Hamilton spaces.
Generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds
We consider generalized m-quasi-Einstein metric within the framework of Sasakian and K-contact manifolds. First, we prove that a complete Sasakian manifold M admitting a generalized m-quasi-Einstein metric is compact and isometric to the unit sphere . Next, we generalize this to complete K-contact manifolds with m ≠ 1.
Generalized plane wave manifolds
Generalized PN manifolds and separation of variables
The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.
Generalized pointwise symmetric spaces
Generalized polarized manifolds.
Generalized P-reducible (α,β)-metrics with vanishing S-curvature
We study one of the open problems in Finsler geometry presented by Matsumoto-Shimada in 1977, about the existence of a concrete P-reducible metric, i.e. one which is not C-reducible. In order to do this, we study a class of Finsler metrics, called generalized P-reducible metrics, which contains the class of P-reducible metrics. We prove that every generalized P-reducible (α,β)-metric with vanishing S-curvature reduces to a Berwald metric or a C-reducible metric. It follows that there is no concrete...
Generalized projective geometries: General theory and equivalance with Jordan structures.
Generalized -space-forms
Generalized symmetric spaces and minimal models
We prove that any compact simply connected manifold carrying a structure of Riemannian 3- or 4-symmetric space is formal in the sense of Sullivan. This result generalizes Sullivan's classical theorem on the formality of symmetric spaces, but the proof is of a different nature, since for generalized symmetric spaces techniques based on the Hodge theory do not work. We use the Thomas theory of minimal models of fibrations and the classification of 3- and 4-symmetric spaces.
Generalized symmetric spaces (Preliminary communication)