18 citations · 72 across the 36 of their papers we have counts for
42 papers
Willmore-type variational problem for foliated hypersurfaces
Vladimir Rovenski
We study new Willmore-type variational problem for a hypersurface in equipped with an -dimensional foliation . Its general version is the Reilly…
Steady flows of ideal incompressible fluid
Vladimir Yu. Rovenski, Vladimir A. Sharafutdinov
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the…
Integral formulas for a foliated sub-Riemannian manifold
Vladimir Rovenski
In this article, we deduce a series of integral formulas for a foliated sub-Riemannian manifold, which is a new geometric concept denoting a Riemannian manifold equipped with a dis…
A series of integral formulas for a foliated sub-Riemannian manifold
Vladimir Rovenski
In this article, we prove a series of integral formulae for a codimension-one foliated sub-Riemannian manifold, i.e., a Riemannian manifold equipped with a distribution ${\…
On Ricci curvature of metric structures on -manifolds
Vladimir Rovenski, Robert Wolak
We study the properties of Ricci curvature of -manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci…
On non-gradient -quasi-Einstein contact metric manifolds
Dhriti Sundar Patra, Vladimir Rovenski
Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the -quasi-Einstein struct…
On the mixed scalar curvature of almost multi-product manifolds
Vladimir Rovenski
A pseudo-Riemannian manifold endowed with orthogonal complementary distributions (called a Riemannian almost multi-product structure) appears in such topics as multiply warpe…
The Einstein-Hilbert type action on almost -product manifolds
Vladimir Rovenski
A Riemannian manifold endowed with orthogonal complementary distributions (called here a Riemannian almost -product structure) appears in such topics as multiply warped pr…
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,…
Almost -Ricci solitons on Kenmotsu manifolds
Dhriti Sundar Patra, Vladimir Rovenski
In this paper we characterize the Einstein metrics in such broader classes of metrics as almost -Ricci solitons and -Ricci solitons on Kenmotsu manifolds, and generalize some…
Integral formulas for a Riemannian manifold with several orthogonal complementary distributions
Vladimir Rovenski
In the paper we prove integral formulae for a Riemannian manifold endowed with orthogonal complementary distributions, which generalize well-known formula for and give…
The Einstein-Hilbert type action on metric-affine almost-product manifolds
Vladimir Rovenski, Tomasz Zawadzki
We continue our study of the mixed Einstein-Hilbert action as a functional of a pseudo-Riemannian metric and a linear connection. Its geometrical part is the total mixed scalar cur…
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…
The curve shortening flow in the metric-affine plane
Vladimir Rovenski
We investigate for the first time the curve shortening flow in the metric-affine plane and prove that under simple geometric condition it shrinks a closed convex curve to a "round…
Deforming convex bodies in Minkowski geometry
Vladimir Rovenski, Pawel Walczak
We introduce and study deformation of Minkowski norms in , determined by a set of linearly independent 1-forms and a smooth…
Variations of the Godbillon--Vey invariant of transversely parallelizable foliations
Vladimir Rovenski, Paweł Walczak
We consider a -dimensional smooth manifold equipped with a -dimensional, a priori non-integrable, distribution and a -vector field ${\bf T}=T_1\wed…
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…
An integral formula for a pair of singular distributions
Paul Popescu, Vladimir Rovenski
The paper is devoted to differential geometry of singular distributions (i.e., of varying dimension) on a Riemannian manifold. Such distributions are defined as images of the tange…
The Partial Ricci Flow on -foliations
Vladimir Rovenski, Robert Wolak
In the paper we introduce new metric structures on -foliations that are less rigid than the well-known structures: almost contact and 3-quasi-Sasakian structures as w…
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…
The weighted mixed curvature of a foliated manifold
Vladimir Rovenski
In this paper, we introduce the weighted mixed (sectional, Ricci and scalar) curvature of a foliated (and almost-product) Riemannian manifold equipped with a vector field $…
A Godbillon-Vey type invariant for a 3-dimensional manifold with a plane field
Vladimir Rovenski, Pawel Walczak
We consider a 3-dimensional smooth manifold equipped with an arbitrary, \textit{a priori} non-integrable, distribution (plane field) and a vector field transvers…
Integral formulas for a metric-affine manifold with two complementary orthogonal distributions
Vladimir Rovenski
We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and i…