کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1840764 | 1031239 | 2012 | 23 صفحه PDF | دانلود رایگان |
We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperkähler, are analogs of the hypercomplex, hyperhermitian and hyperkähler structures in the definite case. We show that a compact 4-manifold carries a para-hyperkähler structure iff it has a metric of split signature together with two parallel, null, orthogonal, pointwise linearly independent vector fields. Every compact complex surface admitting a para-hyperhermitian structure has vanishing first Chern class and we show that, unlike the definite case, many of these surfaces carry infinite-dimensional families of such structures. We provide also compact examples of complex surfaces with para-hyperhermitian structures which are not locally conformally para-hyperkähler. Finally, we discuss the problem of non-existence of para-hyperhermitian structures on Inoue surfaces of type S0S0 and provide a list of compact complex surfaces which could carry para-hypercomplex structures.
Journal: Nuclear Physics B - Volume 865, Issue 2, 11 December 2012, Pages 330–352