We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with computable boundary is computable. In fact, we examine the notion of a semi-computable compact set and we prove a more general result: in any computable metric ...

In this paper, we propose a new multi-manifold metric learning (MMML) method for the task of face recognition based on image sets. Different from most existing metric learning algorithms that learn the distance metric for measuring single images, our method aims to learn distance metrics to measure the similarity between manifold pairs. In our method, each image set is modeled as a manifold and...

Abstract The problem of determining the domain closure Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory Lie groupoids natural domains perturbations are found. main novelty that presented method allows us to treat geometries with tangency points. This kind singularity difficult since those points do not have tubular neighbourhood compatible metr...

After a brief review of some basic notions concerning 1–differentiable cohomology, named here d̃-cohomology, we introduce a Lichnerowicz d̃– cohomology in a classical way. Next, following the classical study of coeffective cohomology, a special attention is paid to the study of some problems concerning coeffective cohomology in the graded algebra of 1– differentiable forms. Also, the case of an a...

A contact hypersurface in a Kähler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kähler manifolds. We then apply these general results to obtain classifications of contact hypersurfaces with constant mean curvature in the complex quadric Q = SOn+2/SOnSO2 and its no...

The aim of this paper is to study a contact Riemannian submersion ? : M B between almost metric manifolds such that its total space admits an ??Ricci soliton. Here, we obtain some necessary conditions for which any fiber and the manifold are soliton, Ricci generalized quasi-Einstein, ??Einstein or Einstein. Finally, equipped with torqued vector field give characterizations ?.

We establish a bound for the radius of a tight ball in a, not necessarily closed, contact 3-manifold (M, ξ). The bound is calculated with respect to a Riemannian metric g compatible with an associated contact form α and an almost complex structure on ξ (see [2, 4]). We also consider a weaker form of compatibility and derive similar bounds in this context. In particular we give a Riemannian geom...

Purpose Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object this article to study properties on certain contact metric Design/methodology/approach authors consider almost Kenmotsu 3-manifolds. use local basis manifold that helps terms partial differential equations. Findings First potential vector pointwise collinear with Reeb and prove non-existence suc...