Geodesic
4-Dimensional (Para)-Kähler-Weyl Structures
Publications de l'Institut Mathématique, _N_S_94 (2013) no. 108, p. 91 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
@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 },
     publisher = {mathdoc},
     volume = {_N_S_94},
     number = {108},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2013_N_S_94_108_a8/}
}
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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/