On Riemannian 3-manifolds with distinct constant Ricci eigenvalues.
On Riemannian geometry of tangent sphere bundles with arbitrary constant radius
We shall survey our work on Riemannian geometry of tangent sphere bundles with arbitrary constant radius done since the year 2000.
On space forms of Grassmann manifolds.
On special Riemannian -manifolds with distinct constant Ricci eigenvalues
The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.
On the automorphism group of a second order structure
On the casual structure of homogeneous manifolds.
On the causal structure of Lorentzian Lie groups. A globality theorem for Lorentzian cones in certain solvable Lie algebras.
On the Construction of Codimension Two Minimal Immersions of Exotic Spheres into Euclidean Spheres. II.
On the existence of a codimension 1 completely integrable totally geodesic distribution on a pseudo-Riemannian Heisenberg group.
On the existence of minimal hyperspheres in compact symmetric spaces
On the Finsler geometry of the Heisenberg group and its extension
We first classify left invariant Douglas -metrics on the Heisenberg group of dimension and its extension i.e., oscillator group. Then we explicitly give the flag curvature formulas and geodesic vectors for these spaces, when equipped with these metrics. We also explicitly obtain -curvature formulas of left invariant Randers metrics of Douglas type on these spaces and obtain a comparison on geometry of these spaces, when equipped with left invariant Douglas -metrics. More exactly, we show...
On the geometric rank of homogeneous spaces of nonpositive curvature.
On the geometrical properties of Heisenberg groups
In [20] the existence of major differences about totally geodesic two-dimensional foliations between Riemannian and Lorentzian geometry of the Heisenberg group is proved. Our aim in this paper is to obtain a comparison on some other geometrical properties of these spaces. Interesting behaviours are found. Also the non-existence of left-invariant Ricci and Yamabe solitons and the existence of algebraic Ricci soliton in both Riemannian and Lorentzian cases are proved. Moreover, all of the descriptions...
On the geometry at infinity of the universal covering of
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 induced geometric object on submanifolds of homogeneous spaces
On the invariant method in differential geometry of submanifolds
On the local moduli space of locally homogeneous affine connections in plane domains
Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [5] and [7] for two different versions of the solution.) Using a basic formula by B. Opozda, [7], we prove that all locally homogeneous torsion-less affine connections defined in open domains of a 2-dimensional manifold depend essentially on at most 4 parameters (see Theorem 2.4).
On the meromorphic potential for a harmonic surface in a k-symmetric space.
On the Ricci curvature of homogeneous metrics on noncompact homogeneous spaces.