On the geometry at infinity of the universal covering of
On the geometry of a partial product structure
On the Geometry of Affine Immersions.
On the Geometry of Associated Sheaves
On the geometry of complex Grassmann manifold, its noncompact dual and coherent states.
On the geometry of convex reflectors
In this paper we consider a special class of convex hypersurfaces in Euclidean space which arise as weak solutions to some inverse problems of recovering reflectors from scattering data. For this class of hypersurfaces we study the notion of the focal function which, while sharing the important convexity property with the classical support function, has the advantage of being exactly the "right tool" for such inverse problems. We also discuss briefly the close analogy between one such inverse problem...
On the geometry of frame bundles
Let be a Riemannian manifold, its frame bundle. We construct new examples of Riemannian metrics, which are obtained from Riemannian metrics on the tangent bundle . We compute the Levi–Civita connection and curvatures of these metrics.
On the geometry of free loop spaces.
On the geometry of Goursat structures
A Goursat structure on a manifold of dimension is a rank two distribution such that dim , for , where denote the elements of the derived flag of , defined by and . Goursat structures appeared first in the work of von Weber and Cartan, who have shown that on an open and dense subset they can be converted into the so-called Goursat normal form. Later, Goursat structures have been studied by Kumpera and Ruiz. In the paper, we introduce a new local invariant for Goursat structures, called...
On the Geometry of Goursat Structures
A Goursat structure on a manifold of dimension n is a rank two distribution Ɗ such that dim Ɗ(i) = i + 2, for 0 ≤ i ≤ n-2, where Ɗ(i) denote the elements of the derived flag of Ɗ, defined by Ɗ(0) = Ɗ and Ɗ(i+1) = Ɗ(i) + [Ɗ(i),Ɗ(i)] . Goursat structures appeared first in the work of von Weber and Cartan, who have shown that on an open and dense subset they can be converted into the so-called Goursat normal form. Later, Goursat structures have been studied by Kumpera and Ruiz. In the paper, we introduce...
On the Geometry of Moduli Spaces.
On the geometry of null cones in Einstein-vacuum spacetimes
On the geometry of Riemannian manifolds with a Lie structure at infinity.
On the geometry of some para-hypercomplex Lie groups
In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in...
On the geometry of some solvable extensions of the Heisenberg group
In this paper we first classify left-invariant generalized Ricci solitons on some solvable extensions of the Heisenberg group in both Riemannian and Lorentzian cases. Then we obtain the exact form of all left-invariant unit time-like vector fields which are spatially harmonic. We also calculate the energy of an arbitrary left-invariant vector field on these spaces and obtain all vector fields which are critical points for the energy functional restricted to vector fields of the same length. Furthermore,...
On the geometry of tangent bundles with a class of metrics
We introduce a class of metrics on the tangent bundle of a Riemannian manifold and find the Levi-Civita connections of these metrics. Then by using the Levi-Civita connection, we study the conformal vector fields on the tangent bundle of the Riemannian manifold. Finally, we obtain some relations between the flatness (resp. local symmetry) properties of the tangent bundle and the flatness (resp. local symmetry) on the base manifold.
On the geometry of tangent bundles with the metric II+III
The main purpose of this paper is to investigate some relations between the flatness or locally symmetric property on the tangent bundle TM equipped with the metric II+III and the same property on the base manifold M and study geodesics by means of the adapted frame on TM.
On the geometry of the space of m-pairs of holomorphic subspaces of the n-dimensional projective space ove r an albebra
On the geometry of the standard -symplectic and Poisson manifolds.
On the geometry of two-step nilpotent groups with left invariant Finsler metrics.