9 citations · 19 across the 8 of their papers we have counts for
11 papers
On isometric immersions of almost -product manifolds
Vladimir Rovenski, Pawel Walczak
A Riemannian manifold endowed with complementary pairwise orthogonal distributions is called a Riemannian almost -product manifold. In the article, for the first time, w…
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…
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 formulae for codimension-one foliated Randers spaces
Vladimir Rovenski, Paweł Walczak
Integral formulae for foliated Riemannian manifolds provide obstructions for existence of foliations or compact leaves of them with given geometric properties. This paper continues…
Integral formulae for codimension-one foliated Finsler manifolds
Vladimir Rovenski, Paweł Walczak
We study extrinsic geometry of a codimension-one foliation of a closed Finsler space , in particular, of a Randers space . Using a unit vector field …
Extrinsic geometric flows on foliated manifolds, III
Vladimir Rovenski
We study the geometry of a codimension-one foliation with a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the R…
Extrinsic geometric flows on foliated manifolds, II
Vladimir Rovenski, Pawel Walczak
Extrinsic Geometric Flow (EGF) for a codimension-one foliation has been recently introduced by authors as deformations of Riemannian metrics subject to quantities expressed in term…
Extrinsic geometric flows on foliated manifolds, I
Vladimir Rovenski, Pawel Walczak
We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. W…
Conformal fields and the stability of leaves with constant higher order mean curvature
Krzysztof Andrzejewski, Pawel Walczak
In this paper, we study submanifolds with constant th mean curvature . We investigate, the stability of such submanifolds in the case when they are leaves of a codimension…
Extrinsic curvatures of distributions of arbitrary codimension
Krzysztof Andrzejewski, Pawel Walczak
In this article, using the generalized Newton transformation, we define higher order mean curvatures of distributions of arbitrary codimension and we show that they agree with the…