Pantilie Radu
Institutul de Matematică 'Simion Stoilow' al Academiei Române , C.P. 1-764, 014700, Bucureşti, România.
Proc Math Phys Eng Sci. 2016 Dec;472(2196):20160598. doi: 10.1098/rspa.2016.0598.
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the 'quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the -quaternionic manifolds. Moreover, the notion of 'heaven space' finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a -quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.
受与赋予（全纯）嵌入球面的齐次复流形相对应的四元数几何的启发，我们引入并开始研究“类四元数流形”。作为特殊子类，这些流形包含CR四元数流形和 - 四元数流形。此外，“天堂空间”的概念在这种情况下找到了其适当的一般性水平：（本质上）任何实解析类四元数流形都允许一个（芽）唯一的天堂空间，它是一个 - 四元数流形。我们还给出了赋予嵌入球面的齐次复流形的自然构造，从而强调了类四元数流形的丰富性。
