Analytic atlases on <img src="Edit_948e45b7-cbef-425e-bb79-28648b859994.png" width="23" height="22" alt="" /> can be easily defined making it an n-dimensional complex mani...Analytic atlases on <img src="Edit_948e45b7-cbef-425e-bb79-28648b859994.png" width="23" height="22" alt="" /> can be easily defined making it an n-dimensional complex manifold. Then with the help of bi-M<span style="white-space:nowrap;"><span style="white-space:nowrap;">öbius 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 <img src="Edit_7e5721ee-bb7f-4224-bd52-7d4641ac1c73.png" width="23" height="22" alt="" /> with the two elements group of a fixed point free antianalytic involution of <img src="Edit_ddfdac64-b296-48c5-9bb2-932eb3d76008.png" width="23" height="22" alt="" />. Involutions h(z) of this kind are obtained linearly by composing special M<span style="white-space:nowrap;"><span style="white-space:nowrap;">öbius transformations of the planes with the mapping <img src="Edit_4cda269a-9399-41ae-a5da-0c9d18a419ab.png" width="89" height="24" alt="" /><img src="Edit_4cda269a-9399-41ae-a5da-0c9d18a419ab.png" width="85" height="22" alt="" />. A convenient partition of <img src="Edit_9e899708-41b0-4351-a12b-cc6efb5b1581.png" width="23" height="22" alt="" /> is performed which helps defining an internal operation on <img src="Edit_7cd42987-68f8-4e4c-9382-cbc68b56377e.png" width="49" height="26" alt="" /> and finally actions of the previously defined Lie groups on the non orientable manifold <img src="Edit_5740b48c-f9ea-438d-a87d-8cdc1f83662b.png" width="49" height="25" alt="" /> are displayed.展开更多
文摘Analytic atlases on <img src="Edit_948e45b7-cbef-425e-bb79-28648b859994.png" width="23" height="22" alt="" /> can be easily defined making it an n-dimensional complex manifold. Then with the help of bi-M<span style="white-space:nowrap;"><span style="white-space:nowrap;">öbius 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 <img src="Edit_7e5721ee-bb7f-4224-bd52-7d4641ac1c73.png" width="23" height="22" alt="" /> with the two elements group of a fixed point free antianalytic involution of <img src="Edit_ddfdac64-b296-48c5-9bb2-932eb3d76008.png" width="23" height="22" alt="" />. Involutions h(z) of this kind are obtained linearly by composing special M<span style="white-space:nowrap;"><span style="white-space:nowrap;">öbius transformations of the planes with the mapping <img src="Edit_4cda269a-9399-41ae-a5da-0c9d18a419ab.png" width="89" height="24" alt="" /><img src="Edit_4cda269a-9399-41ae-a5da-0c9d18a419ab.png" width="85" height="22" alt="" />. A convenient partition of <img src="Edit_9e899708-41b0-4351-a12b-cc6efb5b1581.png" width="23" height="22" alt="" /> is performed which helps defining an internal operation on <img src="Edit_7cd42987-68f8-4e4c-9382-cbc68b56377e.png" width="49" height="26" alt="" /> and finally actions of the previously defined Lie groups on the non orientable manifold <img src="Edit_5740b48c-f9ea-438d-a87d-8cdc1f83662b.png" width="49" height="25" alt="" /> are displayed.
