Abstract
The classification of (fξηρ)-structures on differentiable manifolds of even and odd dimensions is given.
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Literature cited
A. L. Bashkene, ”On structures induced on submanifolds of almost complex manifolds,” Liet. Mat. Rinkinys (Lit. Mat. Sb.), No. 1, 23–34 (1976).
A. L. Bashkene, “Tensor structures on surfaces of almost complex manifolds,” in: The VIth All-Union Conference on Contemporary Problems in Geometry, Theses of Rep. of Vilnius Pedag. Inst. [in Russian], Vilnius (1975), pp. 24–25.
R. F. Dombrovskii, “Fields of geometric objects on multidimensional tangentially framed surfaces in Pn,” in: Problems in Geometry [in Russian], Vol. 7 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1975), pp. 153–171.
L. E. Evtushik, Yu. G. Lumiste, N. M. Ostianu, and A. P. Shirokov, “Differential-geometric structures on manifolds,” in: Problems in Geometry [in Russian], Vol. 9 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1979).
G. F. Laptev, “Differential geometry of immersed manifolds. Group-theoretical method of differential-geometric investigations,” Tr. Mosk. Mat. O-va,2, 275–382 (1953).
G. F. Laptev, “Fundamental infinitesimal structures of higher order on a smooth manifold,” in: Proceedings of the Geometry Seminar [in Russian], Vol. 1, VINITI (1966), pp. 139–190.
G. F. Laptev and N. M. Ostianu, “(fξηρ)-Structures on differentiable manifolds,” in: Problems in Geometry [in Russian], Vol. 7 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1975).
A. P. Norden, “Spaces with Cartesian composition,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 117–128. (1963).
N. M. Ostianu, “On submanifolds of spaces with(ϕ, α)-structure,” in: Third Baltic Geometry Conference, Conference Reports [in Russian], Palanga (1968), pp. 119–121.
N. M. Ostianu, “Differential-geometric structures on differentiable manifolds,” in: Problems in Geometry [in Russian], Vol. 8 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1977), pp. 89–111.
N. M. Ostianu, R. F. Dombrovskii, and N. D. Polyakov, “Submanifolds of differentiable manifolds equipped with differential-geometric structures. II. Submanifolds of codimension 2 of contact and almost contact manifolds,” in: Problems in Geometry [in Russian], Vol. 13 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1982), pp. 27–67.
N. M. Ostianu and N. D. Polaykov, “Submanifolds of differentiable manifolds provided with differential-geometric structures. I,” in: Problems in Geometry [in Russian], Vol. 11 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1980), pp. 3–63.
N. D. Polyakov, “Classification of induced (fξηρ)-structures on submanifolds of codimension 2 of an almost-contact manifold,” Moscow State Univ. (1982).
N. D. Polyakov, “Differential-geometric structures on an almost contact manifold,” in: Problems in Geometry [in Russian], Vol. 8 (Itogi Nauki i Tekh. VINITI Akad. Nauk SSSR), Moscow (1977), pp. 113–137.
D. E. Blair, G. D. Ladden, and K. Yano, “Induced structures on submanifolds,” Kodai Math. Sem. Reports,22, No. 2, 188–198 (1970).
R. S. Mishra, “A generalized theory of differential structures,” Tensor,31, No. 2, 155–164 (1977).
M. Okumura, “Certain hypersurfaces of an odd dimensional sphere,” Tohoku Math. J.,19, No. 4, 381–395 (1967).
Y. Watanabe, “Totally umbilical surfaces in normal contact Riemannian manifolds,” Kodai Math. Sem. Reports,19, No. 4, 474–487 (1967).
S. Yamaguchi, “On hypersurfaces in Sasakian manifolds,” Kodai Math. Sem. Reports,21, No. 1, 64–72 (1969).
K. Yano and Ki U-Hang, “On quasinormal (f, g, u, v, λ)-structures,” Kodai Math. Sem. Reports,24, 106–170 (1972).
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Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 14, pp. 57–72, 1983.
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Polyakov, N.D. Classification of (fξηρ)-structures. J Math Sci 28, 182–192 (1985). https://doi.org/10.1007/BF02105210
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DOI: https://doi.org/10.1007/BF02105210