TITLE:
Lie Groups Actions on Non Orientable n-Dimensional Complex Manifolds
AUTHORS:
T. Cao-Huu, D. Ghisa
KEYWORDS:
Analytic Atlas, Complex Manifold, Möbius Transformation, Lie Group Action
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.6,
June
30,
2021
ABSTRACT: Analytic atlases on can be easily defined making it an n-dimensional complex manifold. Then with the help of bi-Möbius transformations in complex coordinates Abelian groups are constructed making this manifold a Lie group. Actions of Lie groups on differentiable manifolds are well known and serve different purposes. We have introduced in previous works actions of Lie groups on non orientable Klein surfaces. The purpose of this work is to extend those studies to non orientable n-dimensional complex manifolds. Such manifolds are obtained by factorizing with the two elements group of a fixed point free antianalytic involution of . Involutions h(z) of this kind are obtained linearly by composing special Möbius transformations of the planes with the mapping . A convenient partition of is performed which helps defining an internal operation on and finally actions of the previously defined Lie groups on the non orientable manifold are displayed.