This is a preview of subscription content, log in via an institution to check access.
Literature cited
K. Leichtweiss, “Zur Riemannschen geometrie Grassmannschen Manifaltigkeiten,” Math. Annalen.,76, 334–366 (1961).
D. Hoffman and R. Osserman, “The geometry of the generalized Gauss map,” Memoirs Amer. Math. Soc.,28, No. 236, 20–30 (1980).
Y. C. Wong, “Differential geometry of the Grassmann manifolds,” Proc. Nat. Acad. Sci. USA,57, 589–594 (1967).
Yu. A. Aminov, “Isometeric immersions of domains of an n-dimensional Lobachevski space into a (2n−1)-dimensional Euclidean space,” Mat. Sb.,3, No. 3, 402–433 (1980).
Yu. A. Aminov, “The Grassmann image of a two-dimensional surface in a four-dimensional Euclidean space,” Ukrain. Geom. Sb., No. 23, 3–16 (1982).
Yu. A. Aminov, “Imbedding problems: geometric and topological aspects,” Itogi Nauki i Tekhniki Akad. Nauk SSSR Ser. Problemy Geom.,13, 119–156 (1982).
A. A. Borisenko and Yu. A. Nikolaevskii, “The classification of the points of multi-dimensional surfaces” in: Theses and Reports of the All-Union Conference on Geometry in the “Large” [in Russian], Novosibirsk (1987), p. 16.
Y. C. Wong, “Sectional curvature of Grassmann manifolds,” Proc. Nat. Acad. Sci. USA,60, No.1, 75–79 (1968).
Sh. Kobayasi and K. Nomidzu, Foundations of Differential Geometry, Interscience Publishers, New York (1969), Vol. 2.
Additional information
Translated from Ukrainskii Geometricheskii Sbornik, No. 32, pp. 11–27, 1989.
Rights and permissions
About this article
Cite this article
Borisenko, A.A., Nikolaevskii, Y.A. Classification of the points of three-dimensional surfaces according to the Grassmann image. J Math Sci 59, 697–709 (1992). https://doi.org/10.1007/BF01097166
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01097166