Banaru, Mihail On totally umbilical cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebra. (English) Zbl 1066.53058 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 41, 7-12 (2002). The author proves that cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra are totally umbilical if and only if they are totally geodesic. Reviewer: Florence Gouli-Andreou (Thessaloniki) Cited in 3 Documents MSC: 53C10 \(G\)-structures 58C05 Real-valued functions on manifolds PDF BibTeX XML Cite \textit{M. Banaru}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 41, 7--12 (2002; Zbl 1066.53058) Full Text: EuDML OpenURL References: [1] Goldberg S.: Totally geodesic hypersurfaces of Kaehler manifolds. Pacif. J. Math. 27, 2 (1968), 275-281. · Zbl 0165.24802 [2] Tashiro Y.: On contact structure of hypersurfaces in complex manifolds. Töhoku Math. J. 15, 1 (1963), 62-78. · Zbl 0126.38003 [3] Kirichenko V. F., Stepanova L. V.: Geometry of hypersurfaces of quasi-Kählerian manifolds. Uspehi Mat. Nauk 2 (1995), 213-214. · Zbl 0866.53042 [4] Stepanova L. V.: Contact geometry of hypersurfaces of quasi-Kählerian manifolds. MSPU ”V. I. Lenin”, Moscow, 1995. · Zbl 0866.53042 [5] Gray A.: Vector cross products on manifolds. Trans. Amer. Math. Soc. 141 (1969), 465-504. · Zbl 0182.24603 [6] Kirichenko V. F.: On nearly-Kählerian structures induced by means of 3-vector cross products on six-dimensional submanifolds of Cayley algebra. Vestnik MGU 3 (1973), 70-75. [7] Blair D. E.: The theory of quasi-Sasakian structures. J. Diff. Geom. 1 (1967), 331-345. · Zbl 0163.43903 [8] Stepanova L. V.: Quasi-Sasakian structure on hypersurfaces of Hermitian manifolds. Scien. Works of MSPU ”V. I. Lenin”, 1995, 187-191. [9] Banaru M.: Hermitian geometry of six-dimensional submanifolds of Cayley algebra. MSPU ”V. I. Lenin”, Moscow, 1993. · Zbl 1031.53087 [10] Kirichenko V. F.: Methods of the generalized Hermitian geometry in the theory of almost contact metric manifolds. Problems of Geometry 18 (1986), 25-71. [11] Gray A.: Some examples of almost Hermitian manifolds. III. J. Math. 10, 2 (1966), 353-366. · Zbl 0183.50803 [12] Cartan E.: Riemannian geometry in an orthogonal frame. MGU, Moscow, 1960. [13] Lichnerowicz A.: Théory globale des connexions et des groupes d’holonomie. Cremonese, Roma, 1955. · Zbl 0116.39101 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.