Abstract
We prove that, in a 6-dimensional Hermitian submanifold of the Cayley algebra, almost contact metric structures are identical on a hypersurface with type number 0 and on a hypersurface with type number 1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banaru M. B., “Geometry of 6-dimensional Hermitian manifolds of the octave algebra,” J. Math. Sci. (New York), vol. 207, no. 3, 354–388 (2015).
Banaru M. B., “On almost contact metric hypersurfaces with type number 1 in 6-dimensional Kähler submanifolds of the Cayley algebra,” Russian Math. (Iz. VUZ), vol. 58, no. 10, 10–14 (2014).
Banaru M. B., “On almost contact metric 1-hypersurfaces in Kählerian manifolds,” Sib. Math. J., vol. 55, no. 4, 585–588 (2014).
Banaru M. B., “The type number of the cosymplectic hypersurfaces of 6-dimensional Hermitian submanifolds of the Cayley algebra,” Sib. Math. J., vol. 44, no. 5, 765–773 (2003).
Banaru M. B., “On Sasakian hypersurfaces in 6-dimensional Hermitian submanifolds of the Cayley algebra,” Sb. Math., vol. 194, no. 8, 1125–1136 (2003).
Kirichenko V. F., “The methods of the generalized Hermitian geometry in the theory of almost contact manifolds,” in: Problems of Geometry [Russian], VINITI, Moscow, 1986, vol. 18, 25–71 (Itogi Nauki i Tekhniki).
Kirichenko V. F., Differential Geometric Structures on Manifolds [Russian], Pechatny?i Dom, Odessa (2013).
Kirichenko V. F., “Classification of Kähler structures induced by 3-vector products in 6-dimensional submanifolds of Cayley algebra,” Izv. Vyssh. Uchebn. Zaved. Mat., no. 8, 32–38 (1980).
Kurihara H., “The type number on real hypersurfaces in a quaternionic space form,” Tsukuba J. Math., vol. 24, 127–132 (2000).
Gray A., “Some examples of almost Hermitian manifolds,” Illinois J. Math., vol. 10, no. 2, 353–366 (1966).
Banaru M., “On the Gray–Hervella classes of AH-structures on six-dimensional submanifolds of Cayley algebra,” God. Sofij. Univ., Fak. Mat. Inform., vol. 95, 125–131 (2004).
Stepanova L. V., “Quasi-Sasakian structure on hypersurfaces in Hermitian manifolds,” Nauch. Tr. MPGU im. V. I. Lenina, 187–191 (1995).
Abu-Saleem A. and Banaru M., “Some applications of Kirichenko tensors,” An. Univ. Oradea, Fasc. Mat., vol. 17, no. 2, 201–208 (2010).
Banaru M. B., “Hermitian geometry of 6-dimensional submanifolds of the Cayley algebra,” Sb. Math., vol. 193, no. 5, 635–648 (2002).
Kirichenko V. F., “The Hermitian geometry of the six-dimensional symmetric submanifolds of a Cayley algebra,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., no. 3, 6–13 (1994).
Banaru M. B. and Kirichenko V. F., “The Hermitian geometry of the 6-dimensional submanifolds of a Cayley algebra,” Russian Math. Surveys, vol. 49, no. 1, 223–224 (1994).
Abu-Saleem A. and Banaru M. B., “On almost contact metric hypersurfaces of nearly Kählerian 6-sphere,” Malaysian J. Math. Sci., vol. 8, no. 1, 35–46 (2014).
Banaru M. B. and Banaru G. A., “A note on almost contact metric hypersurfaces of nearly Kählerian 6-sphere,” Bull. Transilv. Univ. Braşov, Ser. III. Math., Inform., Phys., vol. 8, no. 2, 21–28 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Smolensk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 4, pp. 721–727, July–August, 2017
Rights and permissions
About this article
Cite this article
Banaru, M.B. On almost contact metric hypersurfaces with type number 1 or 0 in 6-dimensional Hermitian submanifolds of the Cayley algebra. Sib Math J 58, 559–563 (2017). https://doi.org/10.1134/S0037446617040012
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446617040012