Hermitian metrics of semi-negative curvature on quotients of bounded symmetric domains.
Higher Equivariant Index Theorem for Homogeneous spaces.
Higher order torsions of spaces with Cartan connection
Hodge numbers and invariant complex structures of compact nilmanifolds
In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.
Hodge theory for twisted differentials
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds in class C of Fujiki, first stated by D. Arapura.
Homogeneity of infinite dimensional isoparametric submanifolds.
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 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 hessian manifolds
A flat affine manifold is said to Hessian if it is endowed with a Riemannian metric whose local expression has the form where is a -function and is an affine local coordinate system. Let be a Hessian manifold. We show that if is homogeneous, the universal covering manifold of is a convex domain in and admits a uniquely determined fibering, whose base space is a homogeneous convex domain not containing any full straight line, and whose fiber is an affine subspace of .
Homogeneous -symmetric spaces of interior type with simple real fundamental groups and their connection with parabolic spaces.
Homogeneous Kähler manifolds admitting a transitive solvable group of automorphisms
Homogeneous Lorentzian structures on some Gödel-Levichev's spacetimes, and associated reductive decompositions.
Homogeneous quaternionic Kähler structures on Alekseevskian 𝒲-spaces
The homogeneous quaternionic Kähler structures on the Alekseevskian 𝒲-spaces with their natural quaternionic structures, each of these spaces described as a solvable Lie group, and the type of such structures in Fino's classification, are found.
Homogeneous Randers spaces admitting just two homogeneous geodesics
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was investigated and positively answered in previous papers. It is conjectured that this result can be improved, namely that any homogeneous Finsler manifold admits at least two homogenous geodesics. Examples of homogeneous Randers manifolds admitting just two homogeneous geodesics are presented.
Homogeneous Riemannian manifolds with generic Ricci tensor
We describe homogeneous manifolds with generic Ricci tensor. We also prove that if 𝔤 is a 4-dimensional unimodular Lie algebra such that dim[𝔤,𝔤] ≤ 2 then every left-invariant metric on the Lie group G with Lie algebra 𝔤 admits two mutually opposite compatible left-invariant almost Kähler structures.