Spontaneous compactification of subspaces

A mechanism of spontaneous compactification, based on a requiement of parallelizability of gauge fields potentials in relation to general (riemann and gauge) connection that results in the connection of the group of gauge fields transformations with the holonomy group of iemann connection is considered. A lagrangian is considered corresponding to vacuum state of all fields except of Eisntein fields and gauge fields. The lagrangian includes a spontaneous transition with flat space transformation into compact symmetrical spaces at n=3 for time-like and at n>4 for space-like additional measurements. Gauge fields providing the mechanism of spontaneous compactification during interaction with Einstein fields reffer to the gauge group coinciding with the group of Riemann connection holonomy