Related papers: Lifts of Structures on Product Manifolds
The present paper aims to study the higher-order complete and vertical lifts of the extended almost complex structures on an extended complex manifold kM. The proposed theorems on the Nijenhuis tensor of an extended almost complex structure…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We…
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
The purpose of the present work is to study the complete and horizontal lifts of the metallic structure on tangent bundles with respect to almost product structure. We also establish fundamental formulae related to integrability and…
The present paper is devoted to some results concerning with the complete lifts of an almost complex structure and a connection in a manifold to its (0,q)-tensor bundle along the corresponding cross-section.
We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to…
Concepts and techniques from the theory of G-structures of higher order are applied to the study of certain structures (volume forms, conformal structures, linear connections and projective structures) defined on a pseudo-Riemanniann…
We provide an upper bound on the topological complexity of twisted products. We use it to give an estimate $$TC(X)\le TC(\pi_1(X))+\dim X$$ of the topological complexity of a space in terms of its dimension and the complexity of its…
We show that on an arbitrary collection of objects there is a wide variety of higher order architectures governed by hyperstructures. Higher order gluing, local to global processes, fusion of collections, bridges and higher order types are…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from…
We establish a parametric extension $h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the $3$-dimensional result from \cite{Eli89}. It implies, in particular, that any…
We construct "higher" motion planners for automated systems whose space of states are homotopy equivalent to a polyhedral product space $Z(K,\{(S^{k_i},\star)\})$, e.g. robot arms with restrictions on the possible combinations of…
We consider some natural (functorial) lifts of geometric objects associated with statistical manifolds (metric tensor, dual connections, skewness tensor, etc.) to higher tangent bundles. It turns out that the lifted objects form again a…
We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product…
We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads.
In the first part we survey some of the known results and conjectures on compact Hyperkaehler (HK) manifolds. In the second part we presents a program which aims to show that HK four-folds whose second cohomology (with 4-tuple cup-product)…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…