Varieties with a degenerate Gauss mapping with multiple foci, and twisted cones
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2003), pp. 3-14.

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M. A. Akivis; V. V. Goldberg. Varieties with a degenerate Gauss mapping with multiple foci, and twisted cones. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2003), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2003_11_a0/

[1] Fischer G., Piontkowski J., Ruled varieties. An introduction to algebraic differential geometry, Advanced Lect. Math., Friedr. Vieweg Sohn, Braunschweig, 2001, 142 pp. | MR

[2] Landsberg J. M., Algebraic geometry and projective differential geometry, Lect. Notes Series, 45, Seoul National Univ., 1999, 85 pp. | MR | Zbl

[3] Chern S. S., Kuiper N. H., “Some theorems on isometric imbeddings of compact Riemannian manifolds in Euclidean space”, Ann. Math. Ser. 2, 56 (1952), 422–430 | DOI | MR

[4] Delanoë Ph., “L'opérateur de Monge–Ampère réel t la géométrie des sous-varoétés”, Geometry and Topology of Submanifolds, eds. Morvan J. M., Verstraelen L., World Sci., 1989, 49–72 | MR

[5] Ishikawa G., “Developable hypersurfaces and algebraic homogeneous spaces in real projective space”, Homogeneous structures and theory of submanifolds, no. 1069, Sūrikaisekikenkyūsho Kōkyūroku, Kyoto, 1998, 92–104 | MR

[6] Ishikawa G., “Developable hypersurfaces and homogeneous spaces in a real projective space”, Lobachevskii J. Math., 3 (1999), 113–125 | MR | Zbl

[7] Cartan É., “La deformation des hypersurfaces dans l'espace euclidien reel à $n$ dimensions”, Bull. Soc. Math. France, 44 (1919), 65–99 | MR

[8] Cartan É., “Sur les variétés de courbure constante d'un espace euclidien ou non-euclidien”, Bull. Soc. Math. France, 47 (1919), 125–160 | MR

[9] Cartan É., “Sur les variétés de courbure constante d'un espace euclidien ou non-euclidien”, Bull. Soc. Math. France, 48 (1920), 132–208 | MR | Zbl

[10] Akivis M. A., Goldberg V. V., Projective differential geometry of submanifolds, North-Holland, Amsterdam, 1993, 362 pp. | MR | Zbl

[11] Akivis M. A., Goldberg V. V., “On the structure of submanifolds with degenerate Gauss maps”, Geom. Dedic., 86:1–3 (2001), 205–226 | DOI | MR | Zbl

[12] Griffiths P. A., Harris J., “Algebraic geometry and local differential geometry”, Ann. Sci. École Norm. Sup. Ser. 4, 12 (1979), 355–452 | MR | Zbl

[13] Akivis M. A., Goldberg V. V., “An affine analogue of the Hartman-Nirenberg cylinder theorem”, Math. Ann., 323:3 (2002), 573–582 | DOI | MR

[14] Wu H., Zheng F., “On complete developable submanifolds in complex Euclidean spaces”, Comm. Anal. Geom., 10:3 (2002), 611–646 | MR | Zbl

[15] Piontkowski J., “Developable varieties with all singularities at infinity”, Manuscr. Math., 106 (2001), 75–99 | DOI | MR | Zbl

[16] Piontkowski J., Affinely smooth developable varieties of Gauss rank $3$ and $4$, Preprint, 2001, 19 pp. | MR

[17] Sacksteder R., “On hypersurfaces with no negative sectional curvature”, Amer. J. Math., 82:3 (1960), 609–630 | DOI | MR | Zbl

[18] Wu H., “Complete developable submanifolds in real and complex Euclidean spaces”, Intern. J. Math., 6:3 (1995), 461–489 | DOI | MR | Zbl

[19] Ishikawa G., “Singularities of developable surfaces”, Singularity Theory (Liverpool, 1996), London Math. Soc. Lecture Note Ser., 263, Cambridge Univ. Press, 1999, 403–418 | MR | Zbl

[20] Akivis M. A., Goldberg V. V., “Local equivalence of Sacksteder and Bourgain hypersurfaces”, Hokkaido Math. J., 30:3 (2001), 661–670 | MR | Zbl

[21] Akivis M. A., Goldberg V. V., “The geometry of lightlike hypersurfaces of the de Sitter space”, Acta Appl. Math., 53:3 (1998), 297–328 | DOI | MR | Zbl

[22] Akivis M. A., Goldberg V. V., “Singular points of lightlike hypersurfaces of the de Sitter space”, Publ. Inst. Math. N.S. (Beograd), 63:77 (1998), 81–101 | MR | Zbl

[23] Akivis M. A., Goldberg V. V., “The geometry of lightlike hypersurfaces on manifolds endowed with a conformal structure of Lorentzian signature”, Differential Geometry and Applications (1998, Berlin–Brno), Mazaryk Univ., Brno, 1999, 161–170 | MR

[24] Akivis M. A., Goldberg V. V., “Lightlike hypersurfaces on manifolds endowed with a conformal structure of Lorentzian signature”, Acta Appl. Math., 57:3 (1999), 255–285 | DOI | MR | Zbl

[25] Bryant R. L., Chern S. S., Gardner R. B., Goldsmith H. L., Griffiths P. A., Exterior differential systems, Springer-Verlag, New York, 1991, 475 pp. | MR

[26] Akivis M. A., “O mnogomernykh strogo parabolicheskikh poverkhnostyakh”, Izv. vuzov. Matematika, 1987, no. 5, 3–10 | MR | Zbl