EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 94(108), pp. 91–98 (2013)

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Peter Gilkey, Stana Nikcevic

Mathematics Department, University of Oregon, Eugene OR 97403, USA; Mathematical Institute SANU, Beograd, Serbia

Abstract: 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.

Keywords: Weyl geometry; Hermitian manifold; para-Hermitian manifold; pseudo-Hermitian manifold; Kähler manifold; para-Kähler manifold; 4-dimensional geometry

Classification (MSC2000): 53B05; 15A72, 53A15, 53C07

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Electronic fulltext finalized on: 8 Nov 2013. This page was last modified: 22 Nov 2013.

© 2013 Mathematical Institute of the Serbian Academy of Science and Arts
© 2013 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition