Holonomy Groups of a Fully Parallelizable Manifold
Holonomy groups of complete flat manifolds
We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set and that each element of is represented by a manifold with finite holonomy group.
Holonomy groups of five dimensional Bieberbach groups.
Holonomy orbits of the snake charmer algorithm
Holonomy theory and 4-dimensional Lorentz manifolds.
Holonomy, twisting cochains and characteristic classes
This paper contains a description of various geometric constructions associated with fibre bundles, given in terms of important algebraic object, the “twisting cochain". Our examples include the Chern-Weil classes, the holonomy representation and the so-called cyclic Chern character of Bismut and others (see [2, 11, 27]), also called the Bismut’s class. The later example is the principal one for us, since we are motivated by the attempt to find an algebraic approach to the Witten’s index formula....
Homogénéité locale pour les métriques riemanniennes holomorphes en dimension
Une métrique riemannienne holomorphe sur une variété complexe est une section holomorphe du fibré des formes quadratiques complexes sur l’espace tangent holomorphe à telle que, en tout point de , la forme quadratique complexe est non dégénérée (de rang maximal, égal à la dimension complexe de ). Il s’agit de l’analogue, dans le contexte holomorphe, d’une métrique riemannienne (réelle). Contrairement au cas réel, l’existence d’une telle métrique sur une variété complexe compacte n’est...
Homogeneity of infinite dimensional isoparametric submanifolds.
Homogeneous metrical structures on manifold.
Homogeneous bundles and the first eigenvalue of symmetric spaces
In this note we prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kähler metric on a compact Hermitian symmetric spaces of ABCD–type.
Homogeneous -hypersurface-structures on spheres
Homogeneous Cartan geometries
We describe invariant principal and Cartan connections on homogeneous principal bundles and show how to calculate the curvature and the holonomy; in the case of an invariant Cartan connection we give a formula for the infinitesimal automorphisms. The main result of this paper is that the above calculations are purely algorithmic. As an example of an homogeneous parabolic geometry we treat a conformal structure on the product of two spheres.
Homogeneous Cauchy-Riemann structures
Homogeneous Einstein manifolds based on symplectic triple systems
For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved that this is an Einstein manifold.
Homogeneous Einstein metrics on flag manifolds.
Homogeneous Einstein Metrics on Spheres and Proiective Spaces.
Homogeneous Einstein metrics on Stiefel manifolds
A Stiefel manifold is the set of orthonormal -frames in , and it is diffeomorphic to the homogeneous space . We study -invariant Einstein metrics on this space. We determine when the standard metric on is Einstein, and we give an explicit solution to the Einstein equation for the space .
Homogeneous Geodesics in 3-dimensional Homogeneous Affine Manifolds
For studying homogeneous geodesics in Riemannian and pseudo-Riemannian geometry (on reductive homogeneous spaces) there is a simple algebraic formula which works, at least potentially, in every given case. In the affine differential geometry, there is not such a universal formula. In the previous work, we proposed a simple method of investigation of homogeneous geodesics in homogeneous affine manifolds in dimension 2. In the present paper, we use this method on certain classes of homogeneous connections...
Homogeneous geodesics in a three-dimensional Lie group
O. Kowalski and J. Szenthe [KS] proved that every homogeneous Riemannian manifold admits at least one homogeneous geodesic, i.eȯne geodesic which is an orbit of a one-parameter group of isometries. In [KNV] the related two problems were studied and a negative answer was given to both ones: (1) Let be a homogeneous Riemannian manifold where is the largest connected group of isometries and . Does always admit more than one homogeneous geodesic? (2) Suppose that admits linearly independent...
Homogeneous geodesics in five-dimensional generalized symmetric spaces.