4 citations · 12 across the 24 of their papers we have counts for
26 papers
The Harmonic Variational Principle for the Einstein-Hilbert Functional
Sergey Stepanov, Irina Tsyganok
Let (M,g) be a compact n-dimensional Riemannian manifold, n>2. We introduce a restricted variational principle for the Einstein-Hilbert functional by requiring the admissible metri…
A Restricted Chen-Nagano Variational Principle for the Einstein-Hilbert Functional
Sergey Stepanov, Irina Tsyganok
This paper introduces a restricted Chen-Nagano variational principle for the Einstein-Hilbert functional on compact Riemannian manifolds. Instead of considering arbitrary symmetric…
An Inequality Comparing the Dirichlet Energy and the Bienergy of Maps Between Riemannian Manifolds
Sergey Stepanov, Irina Tsyganok
We establish a geometric inequality relating the Dirichlet energy and the bienergy of smooth maps \[ f : (M,g) \to (\overline{M},\overline{g}) \] between Riemanni…
Extensions and Applications of Stein-Weiss Operators to the Study of Traceless Symmetric Tensors
Sergey Stepanov, Irina Tsyganok
First-order differential operators arising from the representation-theoretic decomposition of the covariant derivative play a central role in Riemannian geometry. In this paper, we…
Back to harmonic mappings of compact Riemannian manifolds
Sergey Stepanov, Irina Tsyganok
In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of t…
Geometric Interpretations and Applications of the Berger-Ebin and York -Orthogonal Decompositions
Sergey Stepanov, Irina Tsyganok
The Berger-Ebin and York -orthogonal decompositions of the vector space of symmetric bilinear differential two-forms are fundamental tools in global Riemannian geometry. In th…
Some numerical characteristic inequalities of compact Riemannian manifolds
Sergey Stepanov, Irina Tsyganok
In this paper, we consider numerical characteristics of the connected compact Riemannian manifold (M, g) such as the supremum and infimum of the scalar curvature s, Ricci curvature…
On the theory of minimal submanifolds and harmonic maps from the point of view of the generalized Bochner technique
Sergey Stepanov, Irina Tsyganok
In the present paper, we study harmonic mappings of complete Riemannian manifolds, as well as minimal and stable minimal submanifolds of complete Riemannian manifolds. We examine c…
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…
-decomposition of the second fundamental form of a hypersurface in the study of the general relativistic vacuum constraint equations
Sergey E. Stepanov, Irina I. Tsyganok
In present article, we consider a -orthogonal decomposition of the second fundamental form of a closed spacelike hypersurface in a Lorentzian spacetime and its applications to…
Back to almost Ricci solitons
Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok
In the paper, we study complete almost Ricci solitons using the concepts and methods of geometric dynamics and geometric analysis. In particular, we characterize Einstein manifolds…
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…
Geometry in the large on Hadamard manifolds
Sergey Stepanov, Irina Tsyganok
In this paper, we prove several Liouville-type theorems on the non-existence of Killing-Yano tensors, Killing tensors, and harmonic symmetric tensors on Hadamard manifolds and, in…
From the Ricci flow evolution equation to vanishing theorems for Ricci solitons
Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok
In the paper, we study evolution equations of the scalar and Ricci curvatures under the Hamilton's Ricci flow on a closed manifold and on a complete noncompact manifold. In particu…
On the Betti and Tachibana numbers of compact Einstein manifolds
Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok
Throughout the history of Einstein manifolds, differential geometers have shown great interest in finding the relationships between curvature and the topology of Einstein manifolds…
The Bourguignon Laplacian and harmonic symmetric bilinear forms
Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok
The theory of harmonic symmetric bilinear forms on a Riemannian manifold is an analogue of the theory of harmonic exterior differential forms on this manifold. To show this, we mus…
From harmonic mappings to Ricci flow due to the Bochner technique
Sergey Stepanov, Irina Aleksandrova, Irina Tsyganok
The present paper is devoted to the study a global aspect of the geometry of harmonic mappings and, in particular, infinitesimal harmonic transformations, and represents the applic…
Geometry in the large of the kernel of Lichnerowicz Laplacians and its applications
Vladimir Rovenski, Sergey Stepanov, Irina Tsyganok
There are very few general theorems on the kernel of the well-known Lichnerowicz Laplacian. In the present article we consider the geometry of the kernel of this operator restricte…
From harmonic mappings to Ricci solitons
Sergey Stepanov, Irina Tsyganok
The paper is devoted to the study of the global geometries of harmonic mappings and infinitesimal harmonic transformations and presents their applications to the theory of Ricci so…
Conformal Killing forms on complete Riemannian manifolds with nonpositive curvature operator
Sergey Stepanov, Irina Tsyganok
We give a classification for connected complete locally irreducible Riemannian manifolds with nonpositive curvature operator, which admit a nonzero closed or co-closed conformal Ki…
Liouville-type theorems for conformal mappings and their application
Sergey E. Stepanov, Irina I. Tsyganok
In the present paper we prove Liouville-type theorems: non-existence theorems for conformal mappings of complete Riemannian manifolds. In addition, we give an application of these…
The Killing tensors on an -dimensional manifold with -structure
S. E. Stepanov, I. I. Tsyganok
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine $…
Harmonic Mappings into non-negatively curved Riemannian manifolds
Sergey Stepanov, Irina Tsyganok
Fifty years ago, Eells and Sampson have proved a famous theorem in which they argued that any harmonic mapping is totally geodesic if $(M, g…
A remark on the Laplacian operator which acts on symmetric tensors
S. E. Stepanov, I. I. Tsyganok, I. A. Aleksandrova
More than forty years ago J. H. Samson has defined the Laplacian acting on the space of symmetric covariant -tensors on an -dimensional Riemannian manifold …