Alexander Egoyan. Smooth Infinitesimal Analysis Based Model Of Multidimensional Geometry
Natural Sciences / Mathematics / Geometry
Submitted on: Jul 15, 2012, 07:23:07
Description: In this work a new approach to multidimensional geometry based on smooth infinitesimal analysis (SIA) is proposed. An embedded surface in this multidimensional geometry will look different for the external and internal observers: from the outside it will look like a composition of infinitesimal segments, while from the inside like a set of points equipped by a metric. The geometry is elastic. Embedded surfaces possess dual metric: internal and external. They can change their form in the bulk without changing the internal metric.