Geodesic
4-Dimensional (Para)-Kähler-Weyl Structures
Publications de l'Institut Mathématique, _N_S_94 (2013) no. 108, p. 91 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
@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/}
}
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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/