Banaru, Mihail B. Special Hermitian manifolds and the 1-cosymplectic hypersurfaces axiom. (English) Zbl 1318.53012 Bull. Aust. Math. Soc. 90, No. 3, 504-509 (2014). A special Hermitian manifold is a Hermitian manifold whose Kähler form \(F\) satisfies \(\delta F=0\), where \(\delta\) is the codifferentiation operator. The main result of the paper is that if a special Hermitian manifold \(M\) satisfies the 1-cosymplectic hypersurfaces axiom (i.e., every point of \(M\) belongs to some cosymplectic hypersurface of type one), then \(M\) is a Kähler manifold. Reviewer: Daniel Beltiţă (Bucureşti) Cited in 2 Documents MSC: 53B35 Local differential geometry of Hermitian and Kählerian structures 53B21 Methods of local Riemannian geometry Keywords:cosymplectic structure; special Hermitian manifold; Kähler manifold PDF BibTeX XML Cite \textit{M. B. Banaru}, Bull. Aust. Math. Soc. 90, No. 3, 504--509 (2014; Zbl 1318.53012) Full Text: DOI References: [1] Banaru, Saitama Math. J. 20 pp 1– (2002) [2] Banaru, Taiwanese J. Math. 6 pp 383– (2002) [3] Banaru, J. Harbin Inst. Tech. 8 pp 38– (2000) [4] Abu-Saleem, An. Univ. Oradea Fasc. Mat. 17 pp 201– (2010) [5] Kurihara, Tsukuba J. Math. 24 pp 127– (2000) [6] Banaru, J. Sichuan Univ. Nat. Sci. 26 pp 261– (2003) [7] DOI: 10.1142/8514 · Zbl 1279.53001 · doi:10.1142/8514 [8] DOI: 10.1007/BF01796539 · Zbl 0444.53032 · doi:10.1007/BF01796539 [9] Blair, Progress in Mathematics (2002) [10] Banaru, Annuaire Univ. Sofia Fac. Math. Inform. 95 pp 125– (2004) [11] Banaru, Kyungpook Math. J. 43 pp 27– (2003) [12] Kirichenko, C. R. Acad. Sci. Paris Ser. 1 295 pp 673– (1982) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.