On the existence of killing tensor fields of type q in a compact Riemannian manifold
On the existence of linear connection valued concomitants of geometric objects
On the existence of minimal hyperspheres in compact symmetric spaces
On the existence of multiple geodesics in static space-times
On the existence of parallel normal vector fields of surfaces in
On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions.
On the existence of prolongations of connections by bundle functors.
On the existence of pseudosymmetric Kähler manifolds
It is proved that there exists a non-semisymmetric pseudosymmetric Kähler manifold of dimension 4.
On the Existence of Surfaces with Prescribed Mean Curvature and Boundary.
On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
On the exponential function of an ordered manifold with affine connection.
On the extensor structure of a formulation given by W. Ślebodziński
On the Exterior Capillarity Problem.
On the extremals of a subsidiary capillary problem.
On the - theorems
On the filling radius of positively curved manifolds.
On the finiteness of the fundamental group of a compact shrinking Ricci soliton
Myers's classical theorem says that a compact Riemannian manifold with positive Ricci curvature has finite fundamental group. Using Ambrose's compactness criterion or J. Lott's results, M. Fernández-López and E. García-Río showed that the finiteness of the fundamental group remains valid for a compact shrinking Ricci soliton. We give a self-contained proof of this fact by estimating the lengths of shortest geodesic loops in each homotopy class.
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 first Chern class of a complex submanifold in an almost Hermitian manifold and the normal connection
On the first eigenvalue of spacelike hypersurfaces in Lorentzian space
In this paper we obtain a lower bound for the first Dirichlet eigenvalue of complete spacelike hypersurfaces in Lorentzian space in terms of mean curvature and the square length of the second fundamental form. This estimate is sharp for totally umbilical hyperbolic spaces in Lorentzian space. We also get a sufficient condition for spacelike hypersurface to have zero first eigenvalue.