Harmonic 4-Spaces.
Harmonic curvatures in Lorentzian space.
Harmonic morphisms between degenerate semi-Riemannian manifolds.
Harmonic morphisms between semi-Riemannian manifolds.
Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures
2000 Mathematics Subject Classification: Primary 53B35, Secondary 53C50.In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.
Higher covariant derivatives.
Higher order Codazzi tensors on conformally flat spaces.
Higher order connections.
Higher order contact of real curves in a real hyperquadric
Higher order contact of real curves in a real hyperquadric. II
Let be an Hermitian quadratic form, of maximal rank and index , defined over a complex vector space . Consider the real hyperquadric defined in the complex projective space by Let be the subgroup of the special linear group which leaves invariant and the distribution defined by the Cauchy Riemann structure induced over . We study the real regular curves of constant type in , tangent to , finding a complete system of analytic invariants for two curves to be locally equivalent...
Hodge-Bott-Chern decompositions of mixed type forms on foliated Kähler manifolds
The Bott-Chern cohomology groups and the Bott-Chern Laplacian on differential forms of mixed type on a compact foliated Kähler manifold are defined and studied. Also, a Hodge decomposition theorem of Bott-Chern type for differential forms of mixed type is proved. Finally, the case of projectivized tangent bundle of a complex Finsler manifold is discussed.
Holomorphic Affine and Projective Connections of Hyperbolic Type.
Holomorphic distribution of CR-submanifolds of a complex projective space.
Holomorphically projective curvature tensors
Holomorphically projective mappings of compact semisymmetric manifolds
In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces onto (pseudo-) Kählerian spaces . We proved that in this case space is holomorphically projective flat and is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian...
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
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...
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.