Algebraic Geometry Approach in Theories with Extra Dimensions I. Application of Lobachevsky Geometry

Abstract

This present paper has the purpose to find certain physical appications of Lobachevsky geometry and of the algebraic geometry approach in theories with extra dimensions. It has been shown how the periodic properties of the uniformization functions-solutions of cubic algebraic equations in gravity theory enable the orbifold periodic identification of the points pr{c} and -pr{c} under compactification. It has been speculated that corrections to the extradimensional volume in theories with extra dimensions should be taken into account due to the non-euclidean nature of the Lobachevsky space. It has been demonstrated that in the Higgs mass generation model with two branes (a "hidden" and a "visible" one), to any mass on the visible brane there could correspond a number of physical masses. Algebraic equations for 4D Schwarzschild Black Holes in higher dimensional brane worlds have been obtained.

25 pages; no figures; this is a part of the former hep-th/0511136, but supplemented with an Appendix about the algebraic geometry approach in gravity theory; also some other minor changes in the text and in the formulae enumeration; subm. to Gen. Rel. Grav