Related papers: The B\"acklund Transform of Principal Contact Elem…
The main result is that the qc-scalar curvature of a seven dimensional quaternionic contact Einstein manifold is a constant. In addition, we characterize qc-Einstein structures with certain flat vertical connection and develop their local…
Let S be a compact surface - or the interior of a compact surface - and let V be the manifold of cooriented contact elements of S equiped with its canonical contact structure. A diffeomorphism of V that preserves the contact structure and…
In this paper we introduce the notion of contact angle for an immersed surface in three dimensional sphere. We deduce formulas for the Laplacian and for the Gaussian curvature, and we classify minimal surfaces in $S^3$ with constant contact…
We investigate the local geometry of a pair of independent contact structures on 3-manifolds under maps that independently preserve each contact structure. We discover that such maps are homotheties on the contact 1-forms and we discover…
We review our experiments on the electronic transport properties of atomic contacts between metallic electrodes, in particular superconducting ones. Despite ignorance of the exact atomic configuration, these ultimate quantum point contacts…
Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the…
Motivated by recent experiments on biomimetic membranes exposed to several aqueous phases, we theoretically study the morphology of a membrane in contact with a liquid droplet formed via aqueous phase separation. We concentrate on membranes…
The new integrable mapping with a simple geometric interpretation is presented. This mapping arise from the nonlinear superposition principle for the B\"acklund transformations of some vector evolution equation.
The $B$-connection on almost complex manifolds with Norden metric is an analogue of the first canonical connection of Lihnerovich in Hermitian geometry. In the present paper it is considered a $B$-connection in the class of the…
We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain…
We construct a local action of the group of rational maps from $S^2$ to $GL(n,C)$ on local solutions of flows of the ZS-AKNS $sl(n,C)$-hierarchy. We show that the actions of simple elements (linear fractional transformations) give local…
We show that the discrete principal nets in quadrics of constant curvature that have constant mixed area mean curvature can be characterized by the existence of a K\"onigs dual in a concentric quadric.
Binary symmetry constraints are applied to constructing B\"acklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lower-dimensional Liouville…
The following result is proved: Consider a 4-dimensional Kaehler manifold M with nonvanishing Bochner tensor B. Then any holomorphic transformation of M, which preserves B is a homothety.
We develop the notions of connections and curvature for general Lie-Rinehart algebras without using smoothness assumptions on the base space. We present situations when a connection exists. E.g., this is the case when the underlying module…
We extend the well-known formula for the Euler class of a real oriented even-dimensional vector bundle in terms of the curvature of a metric connection to the case of a general linear connection provided a metric is present. We rewrite the…
All the connections, pure toward the nilpotent structure, are found. Examples of manifolds, for which the curvature tensor is pure or hybrid, are given. For a manifold of B-type a necessary and sufficient condition for purity of the…
We investigate the interaction between single quantum emitters and non-transversally polarised photons for which the electric field vector amplitude has a significant component in the direction of propagation. Even though this situation…
The total curvature of complex hypersurfaces in $\bC^{n+1}$ and its variation in families appear to depend not only on singularities but also on the behaviour in the neighbourhood of infinity. We find the asymptotic loss of total curvature…
We prove some existence results for the Webster scalar curvature problem on the Heisenberg group and on the unit sphere of ${\mathbb C}^{n+1}$, under the assumption of some natural symmetries of the prescribed curvatures. We use variational…