4-Dimensional (Para)-Kähler-Weyl Structures
Publications de l'Institut Mathématique, _N_S_94 (2013) no. 108, p. 91
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We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kähler-Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show any 4-dimensional pseudo-Hermitian manifold also admits a unique Kähler-Weyl structure.
Classification :
53B05 15A72 53A15 53C07
Keywords: Weyl geometry, Hermitian manifold, para-Hermitian manifold, pseudo-Hermitian manifold, Kähler manifold, para-Kähler manifold, 4-dimensional geometry
Keywords: Weyl geometry, Hermitian manifold, para-Hermitian manifold, pseudo-Hermitian manifold, Kähler manifold, para-Kähler manifold, 4-dimensional geometry
Peter Gilkey; Stana Nikčević. 4-Dimensional (Para)-Kähler-Weyl Structures. Publications de l'Institut Mathématique, _N_S_94 (2013) no. 108, p. 91 . http://geodesic.mathdoc.fr/item/PIM_2013_N_S_94_108_a8/
@article{PIM_2013_N_S_94_108_a8,
author = {Peter Gilkey and Stana Nik\v{c}evi\'c},
title = {4-Dimensional {(Para)-K\"ahler-Weyl} {Structures}},
journal = {Publications de l'Institut Math\'ematique},
pages = {91 },
year = {2013},
volume = {_N_S_94},
number = {108},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_2013_N_S_94_108_a8/}
}