Keywords
- Fundamental Form
- Orthogonal Transformation
- Parallel Section
- Normal Vector Field
- Spherical Curvature
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Dillen, F.: The classification of hypersurfaces of a Euclidean space with parallel higher order fundamental form. Math. Z. 203 (1990), 635–643.
Dillen, F.: Sur les hypersurfaces parallèles d'ordre supérieur. C. r. Acad. Sci. Ser. 1, V. 311 (1990), 185–187.
Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vol. I. New York-London: Intersc. Publ., 1963.
Lumiste, Ü.: Small-dimensional irreducible submanifolds with parallel third fundamental form. Tartu Ülikooli Toimetised. Acta et comm. Univ. Tartuensis, No. 734 (1986), 50–62 (Russian).
Lumiste, Ü.: Normally flat submanifolds with parallel third fundamental form. Proc. Estonian Acad. sci. Phys. Math., V. 38, No. 2 (1989), 129–138.
Lumiste, Ü.: Threedimensional submanifolds with parallel third fundamental form in Euclidean spaces. Tartu Ülikooli Toimetised. Acta et comm. Univ. Tartuensis, No. 889 (1990), 45–56.
Lumiste, Ü., Mirzoyan, V.: Submanifolds with parallel third fundamental form. Tartu Ülikooli Toimetised. Acta et comm. Univ. Tartuensis, No. 665 (1984), 42–54 (Russian).
Mirzoyan, V.: Submanifolds with parallel higher order fundamental form. Preprint. Tartu, 1978 (Sov. Math. Rev., 1978, 10A542 Dep.; Russian).
Mirzoyan, V.: Submanifolds with commuting normal vector field. Itogi nauki i techn. VINITI. Probl. geometrii. T. 14 (1983), 73–100 (Russian).
Mirzoyan, V.: On submanifolds with parallel fundamental form αS (s ≥ 3). Tartu Ülikooli Toimetised. Acta et comm. Univ. Tartuensis (to appear; Russian).
Nomizu, K., Ozeki, H.: A theorem on curvature tensor fields. Proc. Nat. Sci. USA, V. 48 (1962), 206–207.
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© 1991 Springer-Verlag
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Lumiste, Ü. (1991). On Submanifolds with parallel higher order fundamental form in euclidean spaces. In: Ferus, D., Pinkall, U., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 1481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083636
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DOI: https://doi.org/10.1007/BFb0083636
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