额外维理论中的代数几何方法I。罗巴切夫斯基几何的应用
Algebraic Geometry Approach in Theories with Extra Dimensions I. Application of Lobachevsky Geometry
摘要：
本文的目的是寻找罗巴切夫斯基几何和代数几何方法在额外维理论中的某些物理应用。它已被证明如何在引力理论中的三次代数方程的解的均匀化函数的周期性质，使轨道周期识别的点pr{c}和-pr{c}下紧化。有人推测，由于罗巴切夫斯基空间的非欧性质，在额外维度理论中对额外维度体积的修正应该被考虑在内。已经证明，在希格斯质量生成模型中，有两个膜（一个“隐藏”膜和一个“可见”膜），可见膜上的任何质量都可以对应许多物理质量。得到了高维膜世界中四维Schwarzschild黑洞的代数方程。
英文摘要：
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.
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