10 citations · 16 across the 10 of their papers we have counts for
10 papers · 1 filter
On minimal hypersurfaces in Euclidean spaces and Riemannian manifolds
Josef Mikes, Sergey Stepanov, Irina Tsyganok
This paper establishes the conditions under which minimal and stable minimal hypersurfaces are characterized as hyperplanes in Euclidean spaces and as totally geodesic submanifolds…
New applications of the Ahlfors Laplacian
Sergey E. Stepanov, Josef Mikes, Irina I. Tsyganok
In this article, we consider an orthogonal decomposition of the traceless part of the Ricci tensor of a compact Riemannian manifold and study its application to the geometry of com…
On higher order Codazzi tensors on complete Riemannian manifolds
I. G. Shandra, S. E. Stepanov
We prove several Liouville-type non-existence theorems for higher order Codazzi tensors and classical Codazzi tensors on complete and compact Riemannian manifolds, in particular. T…
On the existence of pre-semigeodesic coordinates
Irena Hinterleitner, Josef Mikeš
In the present paper we consider the problem of the existence of pre-semigeodesic coordinates on manifolds with affine connection. We proved that pre-semigeodesic coordinates exist…
Eigenvalues of the Tachibana Operator which Acts on Differential Forms
Sergey E. Stepanov, Josef Mikes
In the present paper we show spectral properties of a littleknown natural Riemannian second-order differential operator acting on differential forms.
Geodesic mappings of (pseudo-) Riemannian manifolds preserve the class of differentiability
I. Hinterleitner, J. Mikeš
In this paper we prove that geodesic mappings of (pseudo-) Riemannian manifolds preserve the class of differentiability \hbox{}. Also, if the Einstein space ad…
Betti and Tachibana numbers
S. E. Stepanov, J. Mikeš
We present a rough classification of differential forms on a Riemannian manifold, we consider definitions and properties of conformal Killing forms on a compact Riemannian manifold…
Geodesic Mappings and Einstein Spaces
Irena Hinterleitner, Josef Mikeš
In this paper we study fundamental properties of geodesic mappings with respect to the smoothness class of metrics. We show that geodesic mappings preserve the smoothness class of…
Reconstruction of the connection or metric from some partial information
J. Mikeš, A. Vanžurová
In a neighborhood of a (positive definite) Riemannian space in which special, semigeodesic, coordinates are given, the metric tensor can be calculated from its values on a suitable…
Fundamental PDE's of the Canonical Almost Geodesic Mappings of Type
V. E. Berezovski, J. Mikeš, A. Vanžurová
For modelling of various physical processes, geodesic lines and almost geodesic curves serve as a useful tool. Trasformations or mappings between spaces (endowed with a metric or c…