Euclidean geometry as algorithm for construction of generalized geometries

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dc.creatorRylov, Yuri A.
dc.date2005-11-23
dc.date.accessioned2026-07-07T06:51:38Z
dc.date.available2026-07-07T06:51:38Z
dc.descriptionIt is shown that the generalized geometries may be obtained as a deformation of the proper Euclidean geometry. Algorithm of construction of any proposition S of the proper Euclidean geometry E may be described in terms of the Euclidean world function sigma_E in the form S(sigma_E). Replacing the Euclidean world function sigma_E by the world function sigma of the geometry G, one obtains the corresponding proposition S(sigma) of the generalized geometry G. Such a construction of the generalized geometries (known as T-geometries) uses well known algorithms of the proper Euclidean geometry and nothing besides. This method of the geometry construction is very simple and effective. Using T-geometry as the space-time geometry, one can construct the deterministic space-time geometries with primordially stochastic motion of free particles and geometrized particle mass. Such a space-time geometry defined properly (with quantum constant as an attribute of geometry) allows one to explain quantum effects as a result of the statistical description of the stochastic particle motion (without a use of quantum principles).
dc.description22 pages, 0 figures
dc.identifierhttps://arxiv.org/abs/math/0511575
dc.identifierhttp://arxiv.org/abs/math/0511575
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105053
dc.subjectGeneral Mathematics
dc.subject03B30; 51K99
dc.titleEuclidean geometry as algorithm for construction of generalized geometries
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