Abstract:
We study the minimality of an isometric immersion of a Riemannian manifold into a strictly pseudoconvex CR manifold endowed with the Webster metric hence formulate a version of the CR Yamabe problem for CR manifolds-with-boundary. This is shown to be a nonlinear subelliptic problem of variational origin.

Abstract:
We adopt the methods of pseudohermitian geometry (cf. [16]) to study the tangent sphere bundle U(M) over a Riemannian manifold M. If M is an elliptic space form of sectional curvature 1 then U(M) is shown to be globally pseudo-Einstein (in the sense of J. M. Lee, [12]).

Abstract:
We prove Caccioppoli type estimates and consequently establish local H？lder continuity for a class of weak contact -harmonic maps from the Heisenberg group into the sphere . 1. Introduction The study of pseudoharmonic maps was started by Barletta et al. [1] (cf. also [2, 3] for successive investigations) as a generalization of the theory of harmonic maps among Riemannian manifolds (cf., e.g., [4]) and by identifying the results of Jost and Xu [5], Zhou [6], Haj？asz and Strzelecki [7], and Wang [8] as local aspects of the theory of pseudoharmonic maps from a strictly pseudoconvex CR manifold into a Riemannian manifold (cf. also [9, pages 225-226]). A similar class of maps, yet with values in another CR manifold, was studied in [10]. These are critical points of the functional where is a compact strictly pseudoconvex CR manifold of CR dimension ,？？ , and is a contact form on . Also is a contact Riemannian manifold and in particular an almost CR manifold (of CR codimension ). A moment's thought reveals the augmented difficulties such a theory may present. For instance, if and are two strictly pseudoconvex CR manifolds endowed, respectively, with contact forms and , then the pseudohermitian analog of the notion of a harmonic morphism (among Riemannian manifolds) is quite obvious: one may consider continuous maps such that the pullback of any local solution to in satisfies in in distribution sense. Here and are the sublaplacians of and , respectively. Unlike the situation in [2] (where the target manifold is Riemannian and pulls back local harmonic functions on to distribution solutions of ) such is not necessarily smooth (since it is unknown whether local coordinate systems on such that in might be produced). To give another example, should one look for a pseudohermitian analog to the Fluglede-Ishihara theorem (cf. [3] when is CR and is Riemannian), one would face the lack of an Ishihara type lemma (cf. [11]) as it is unknown whether admits local solutions whose (horizontal) gradient and hessian have prescribed values at a point. Moreover, what would be the appropriate notion of a hessian (cf. [12] for a possible choice)? A third example, discussed at some length in this paper, is that of the “degeneracy” of the Euler-Lagrange equations associated to the variational principle when is a Sasakian manifold. Indeed the matrix has but rank at each point (a well-known phenomenon in contact Riemannian geometry, cf., e.g., [13]. See also [14]). Consequently, in general one may not expect regularity of weak solutions to (2). For instance, if is the Heisenberg group

Abstract:
We show that any contact form whose Fefferman metric admits a nonzero parallel vector field is pseudo-Einstein of constant pseudohermitian scalar curvature. As an application we compute the curvature groups of the total space of the canonical circle bundle over a CR manifold.

Abstract:
We study subelliptic biharmonic maps, i.e. smooth maps from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of a certain bienergy functional. We show that a map is subelliptic biharmonic if and only if its vertical lift to the (total space of the) canonical circle bundle is a biharmonic map with respect to the Fefferman metric.

Abstract:
The main result we obtain is that given €:N ￠ ’M a Ts-subbundle of the generalized Hopf fibration € ˉ:H2n+s ￠ ’ ￠ Pn over a Cauchy-Riemann product i:M ￠ ￠ Pn, i.e. j:N ￠ H2n+s is a diffeomorphism on fibres and € ˉ ￠ j=i ￠ €, if s is even and N is a closed submanifold tangent to the structure vectors of the canonical ￠ -structure on H2n+s then N is a Cauchy-Riemann submanifold whose Chen class is non-vanishing.

Abstract:
The paper present a way of checking and optimization of a demolition scenario at an industrial building based on controlled blasting method in order to transition to the actual demolition of the building in question. For this purpose we used a specialized computer system that describes the behaviour of the structure at exceptional actions, from the application of forces, the opening and propagation of cracks, the separation structural elements up to total collapse of the building.