4 citations · 5 across the 5 of their papers we have counts for
5 papers · 1 filter
Note on the conjecture of D.Blair in contact Riemannian geometry
Vladimir Krouglov
The conjecture of D.Blair says that there are no nonflat Riemannian metrics of nonpositive curvature compatible with a contact structure. We prove this conjecture for a certain cla…
Local Equivalence Problem for Sub-Riemannian Structures
Vladimir Krouglov
We solve the local equivalence problem for sub-Riemannian structures on (2n + 1)-dimensional manifolds. We show that two sub-Riemannian structures are locally equivalent if and onl…
On the extrinsic geometry of contact structures
Vladimir Krouglov
In the paper we prove, that extrinsic curvature does not impose restrictions on the topology of a contact structure, except the obvious ones.
Parabolic foliations on 3-manifolds
Vladimir Krouglov
In the paper we prove that every closed orientable three-manifold admits a parabolic foliation.
The curvature of contact structure on 3-manifolds
Vladimir Krouglov
We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a coroll…