d-objects kinematics on smooth manifolds
Sergey S.Kokarev
TL;DR
This paper develops the kinematic theory of deformational structures called d-objects on smooth manifolds, exploring their algebraic, group, and homotopical properties, and generalizing isometry concepts from Riemannian geometry.
Contribution
It introduces the concept of d-objects deformation and analyzes their algebraic and topological properties, extending isometry theory to broader deformational contexts.
Findings
Established algebraic structures of d-objects deformations
Analyzed group and homotopical properties of deformation sets
Generalized isometry theory for proper deformations
Abstract
The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and investigate group and homotopical properties of the set. In case of proper deformations some propositions, generalizing isometry theory on Riemannian manifolds are formulated.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic and Geometric Analysis · Advanced Differential Geometry Research