18 citations · 72 across the 36 of their papers we have counts for
10 papers · 1 filter
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…