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References
Cecil, T. E. andRyan, P. J.,Focal sets, taut embeddings and the cyclides of Dupin. Math. Ann.236, 177–190 (1978).
Cecil, T. E. andRyan, P. J.,On the number of top-cycles of a tight surface in 3-space. J. London Math. Soc. (2)30. 335–341 (1984).
Cecil, T. E. andRyan, P. J.,Tight and taut immersions of manifolds. Research Notes in Mathematics 107, Boston, London, Melbourne: Pitmann Publ. 1985.
Chen, C.-S.,Tight embedding and projective transformation. Amer. J. Math.101, 1083–1102 (1979).
Chern, S.-S. andLashof, R. K.,On the total curvature of immersed manifolds, II. Mich. Math. J.5, 5–12 (1958).
Donaldson, S. K.,An application of gauge theory to four dimensional topology. J. Differential Geometry18, 279–315 (1983).
Donaldson, S. K.,Connections, cohomology and the intersection from of 4-manifolds. Preprint.
Hebda, J. J.,Some new tight embeddings which cannot be made taut. Geometriae Dedicata17, 49–60 (1984).
Hirsch, M. W.,Immersions of manifolds. Trans. Amer. Math. Soc.83, 242–276 (1959).
Kuiper, N. H.,On surfaces in euclidean three-space. Bull. Soc. Math. Belg.12, 5–22 (1960).
Kuiper, N. H.,Minimal total absolute curvature for immersions. Invent. Math.10, 209–238 (1970).
Kuiper, N. H.,Tight embeddings and maps. Submanifolds of geometrical class three in E N. In: The Chern Symposium 1979. Berlin, Heidelberg, New York: Springer 1980.
Kuiper, N. H. andPohl, W. F.,Tight topological embeddings of the real projective plane in E 5. Inventiones Math.42, 177–199 (1977).
Kulkarni, R. S. andWood, J. W.,Topology of nonsingular complex hypersurfaces. Adv. Math.35, 239–263 (1980).
Lastufka, W. S.,Tight topological immersions of surfaces in Euclidean space. J. Differential Geometry16, 373–400 (1981).
Leichtweiß, K.,Konvexe Mengen. Berlin, Heidelberg, New York: Springer 180.
Milnor, J.,Some consequences of a theorem of Bott. Ann. Math.68, 444–449 (1958).
Milnor, J. andHusemoller, D.,Symmetric Bilinear forms. Ergebnisse der Mathematik 73. Berlin, Heidelberg, New York: Springer 1973.
Milnor, J. W. andStasheff, J. D.,Characteristic classes. Annals of Math. Studies 76. Princeton: Princeton University Press, 1974.
Steenrod, N.,The topology of the fibre bundles. Princeton: Princeton University Press 1951.
Tai, S.-S.,Minimum imbeddings of compact symmetric spaces of rank one. J. Differential Geometry2, 55–66 (1968).
Thorbergsson, G.,Highly connected taut submanifolds. Math. Ann.265, 399–405 (1983).
Thorbergsson, G.,Straffe Untermannigfaltigkeiten in konvexen Hyperflächen. Manuscripta Math.54, 1–15 (1985).
Wall, C. T. C.,Classification of (n - 1)-connected 2n-manifolds. Ann. Math.75, 163–189 (1962).
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Work partially done at IMPA in Rio de Janeiro and supported by the exchange program of GMD (Federal Republic of Germany) and CNPq (Brazil). It was completed at the University of Bonn.
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Thorbergsson, G. Tight immersions of highly connected manifolds. Commentarii Mathematici Helvetici 61, 102–121 (1986). https://doi.org/10.1007/BF02621905
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DOI: https://doi.org/10.1007/BF02621905