Homogeneous Kähler manifolds admitting a transitive solvable group of automorphisms
Homogeneous Lorentz manifolds with simple isometry group.
Homogeneous Lorentzian 3-manifolds with a parallel null vector field.
Homogeneous Lorentzian structures on some Gödel-Levichev's spacetimes, and associated reductive decompositions.
Homogeneous parabolic surfaces in .
Homogeneous Poisson structures on loop spaces of symmetric spaces.
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.
Homogeneous spaces and isoparametric hypersurfaces.
Homogeneous submanifolds of the hyperbolic space.
Homogeneous surfaces in the equiaffine space R⁴
Homogeneous systems of higher-order ordinary differential equations
The concept of homogeneity, which picks out sprays from the general run of systems of second-order ordinary differential equations in the geometrical theory of such equations, is generalized so as to apply to equations of higher order. Certain properties of the geometric concomitants of a spray are shown to continue to hold for higher-order systems. Third-order equations play a special role, because a strong form of homogeneity may apply to them. The key example of a single third-order equation...
Homogeneous totally real submanifolds of complex projective space
Homogeneous variational problems: a minicourse
A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension . In this minicourse we discuss these problems from a geometric point of view.
Homogeneous variational problems and Lagrangian sections
We define a canonical line bundle over the slit tangent bundle of a manifold, and define a Lagrangian section to be a homogeneous section of this line bundle. When a regularity condition is satisfied the Lagrangian section gives rise to local Finsler functions. For each such section we demonstrate how to construct a canonically parametrized family of geodesics, such that the geodesics of the local Finsler functions are reparametrizations.
Homogenization of periodic Finsler metrics.
Homological Mirror Symmetry for manifolds of general type
In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.
Homologie des géodésiques fermées sur des variétés hyperboliques avec bouts cuspidaux
Homology and modular classes of Lie algebroids
For a Lie algebroid, divergences chosen in a classical way lead to a uniquely defined homology theory. They define also, in a natural way, modular classes of certain Lie algebroid morphisms. This approach, applied for the anchor map, recovers the concept of modular class due to S. Evens, J.-H. Lu, and A. Weinstein.