Abstract
Our aim in the present article is to introduce and study new types of retractions of Lobachevsky space. Types of the deformation retracts of Lobachevsky space are presented. The relations between the folding and the deformation retract of Lobachevsky space are deduced. Types of minimal retractions of Lobachevsky space are also presented. Also, the isometric and topological folding in each case and the relation between the deformation retracts after and before folding have been obtained. New types of homotopy maps are deduced. Theorems governing this connection are achieved.
Highlights
Lobachevsky space represents one of the most intriguing and emblematic discoveries in the history of geometry
The aim of this paper is to describe and study new types of retraction, deformation retract and folding the of Lobachevsky space
We start with a metric of the Lobachevsky space L4 in the special spherical Riemann mode S3 Kudryashov [25]
Summary
Lobachevsky space represents one of the most intriguing and emblematic discoveries in the history of geometry. Types of the deformation retracts of Lobachevsky space are presented. The relations between the folding and the deformation retract of Lobachevsky space are deduced .Types of minimal retractions of Lobachevsky space are presented. The isometric and topological folding in each case and the relation between the deformation retracts after and before folding have been obtained.
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