Differential geometry of g-manifolds

  title={Differential geometry of g-manifolds},
  author={Dmitri Alekseevsky and Peter W. Michor},
  journal={Differential Geometry and Its Applications},
Geometric Complexity Theory -- Lie Algebraic Methods for Projective Limits of Stable Points
The primary objective is to understand the points [y], and their stabilizers, which occur in the vicinity of [x] in PV, and an explicit Lie algebra action of G is constructed on a suitably parametrized neighbourhood of x, showing that the Lie algebras of the stabilizers of points in the neighbourhood ofx are parameterized by subspaces of H.
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth con- nected manifold M is locally
Completing Lie algebra actions to Lie group actions
For a finite dimensional Lie algebra $\g$ of vector fields on a manifold $M$ we show that $M$ can be completed to a $G$-space in a unversal way, which however is neither Hausdorff nor $T_1$ in
Cohomology of Horizontal Forms
The complex of s-horizontal forms of a smooth foliation F on a manifold M is proved to be exact for every s = 1, . . . , n = codim F, and the cohomology groups of the complex of its global sections,
Singular Poisson Reduction of Cotangent Bundles
We consider the Poisson reduced space (T Q)/K , where the action of the com pact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T Q. Realizing (T Q)/K
A cotangent bundle Hamiltonian tube theorem and its applications in reduction theory
The Marle-Guillemin-Sternberg (MGS) model is an extremely important tool for the theory of Hamiltonian actions on symplectic manifolds. It has been extensively used to prove many local results both
Geometric foundations of Cartan gauge gravity
We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan
On Heisenberg normal structures
We consider higher dimensional generalisations of normal almost contact structures. Two types of these structures are discussed. In the first case we replace an action of $\mathbb{R}$ (which is the
Local reflexion spaces
A reflexion space is generalization of a symmetric space introduced by O. Loos in [6]. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local


Graded derivations of the algebra of differential forms associated with a connection
The central part of calculus on manifolds is usually the calculus of differential forms and the best known operators are exterior derivative, Lie derivatives, pullback and insertion operators.
In the paper [5], we considered harmonic integrals on local product manifolds, that is, manifolds having two families of submanifolds in complementary dimensions, such that locally they look like the
Curvature-orbits and locally homogeneous riemannian manifolds
We prove that it is possible to associate to each infinitesimal model on a Euclidean vector space V a locally homogeneous Riemannian manifold. As an application, we characterize, in the space of the
On the Existence of Slices for Actions of Non-Compact Lie Groups
If G is a topological group then by a G-space we mean a completely regular space X together with a fixed action of G on X. If one restricts consideration to compact Lie groups then a substantial
Orbits of families of vector fields and integrability of distributions
Let D be an arbitrary set of Cc vector fields on the Cc manifold M. It is shown that the orbits of D are C' submanifolds of M, and that, moreover, they are the maximal integral submanifolds of a
Counter-example to the “Second Singer's theorem”
We give an explicit example showing that a theorem by I. M. Singer announced in [3] (about the existence of a Riemannian homogeneous space with the prescribed curvature tensor and some of its
La géométrie des espaces de Riemann
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Slov ak, Jan, Natural operators in di erential geometry, Springer-Verlag
  • 1993