On the existence of a codimension 1 completely integrable totally geodesic distribution on a pseudo-Riemannian Heisenberg group.
On the existence of pseudosymmetric Kähler manifolds
It is proved that there exists a non-semisymmetric pseudosymmetric Kähler manifold of dimension 4.
On the first Chern class of a complex submanifold in an almost Hermitian manifold and the normal connection
On the geometry of a partial product structure
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 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 Hilbert scheme of points of an almost complex fourfold
If is a complex surface, one has for each the Hilbert scheme , which is a desingularization of the symmetric product . Here we construct more generally a differentiable variety endowed with a stable almost complex structure, for every almost complex fourfold . is a desingularization of the symmetric product .
On the Intrinsic Geometry of Sn x Sn.
On the Kenmotsu hypersurfaces of special Hermitian manifolds.
On the Lebesgue measure of the periodic points of a contact mainfold.
On the persistence of pseudo-holomorphic curves on an almost complex torus (with an appendix by Jügen Pöschel).
On the Riemannian curvature tensor of an almost-product manifold
On the structure vector field of a real hypersurface in complex two-plane Grassmannians
Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure vector field is of Jacobi type.
On the Symplectic Structure of Coadjoint Orbits of (Solvable) Lie Groups and Applications. I.
On the tangent space to the universal Teichmüller space.
On totally umbilical cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebra
On weakly cyclic Ricci symmetric manifolds
We introduce a type of non-flat Riemannian manifolds called weakly cyclic Ricci symmetric manifolds and study their geometric properties. The existence of such manifolds is shown by several non-trivial examples.
On weakly projective symmetric manifolds.