1 citations · 2 across the 9 of their papers we have counts for
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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…
On the Bochner technique for singular distributions
Paul Popescu, Vladimir Rovenski, Sergey Stepanov
In this paper we continue our recent study of a manifold endowed with a singular or regular distribution, determined as the image of the tangent bundle under a smooth endomorphism,…
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…