## Monistic
conception of geometry

## Yuri A. Rylov

*Institute for Problems in Mechanics, Russian
Academy of Sciences*

* 101-1 ,Vernadskii Ave., Moscow, 119526, Russia*

* email: rylov@ipmnet.ru*

Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm

or mirror Web site: http://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated September 15, 2010

#### abstract

One considers
the monistic conception of a geometry, where there is only one fundamental
quantity (world function). All other geometrical quantities a derivative
quantities (functions of the world function). The monisitc conception of a
geometry is compared with pluralistic conceptions of a geometry, where there
are several independent fundamental geometrical quantities. A generalization of
a pluralistic conception of the proper Euclidean
geometry appears to be inconsistent, if the generalized geometry is inhomogeneous. In particular, the Riemannian
geometry appears to be inconsistent, in general, if it is obtained as a
generalization of the pluralistic conception of the Euclidean geometry.

There is
text of the paper in English (pdf, ps) and in Russian (ps, pdf)