Holomorphically pseudosymmetric Kähler metrics on ℂℙⁿ
The aim of this paper is to present examples of holomorphically pseudosymmetric Kähler metrics on the complex projective spaces ℂℙⁿ, where n ≥ 2.
Holomorphicity of Minimal Submanifolds in Complex Space Forms.
Holomorphy angles and sectional curvature in Hermitian elliptic planes over fields and tensor products of fields.
Holonomy and projective equivalence in 4-dimensional Lorentz manifolds.
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 affine hypersurfaces with rank one shape operators.
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.