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Some classifications of ruled submanifolds

김영호|정선미|김동수
대한수학회 (The Korean Mathematical Society)|2014.05|대한수학회보 (Bulletin of the KMS)|제51권 제3호|pp. 823-829

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참고문헌

키워드

Gauss mapruled submanifoldGrassmannian manifold
주제분류수학

초록

Ruled submanifolds in Euclidean space satisfying some algebraic equations concerning the Laplace operator related to the isometric immersion and Gauss map are studied. Cylinders over a finite type curve or generalized helicoids are characterized with such algebraic equations.

Abstract

Ruled submanifolds in Euclidean space satisfying some algebraic equations concerning the Laplace operator related to the isometric immersion and Gauss map are studied. Cylinders over a finite type curve or generalized helicoids are characterized with such algebraic equations.

참고문헌 (12)

  1. C. Baikoussis, "Ruled submanifolds with finite type Gauss map", J. Geom, 49(1-2), pp.42~45 (1994)
  2. C. Baikoussis, "On the Gauss map of ruled surfaces", Glasgow Math. J, 34(3), pp.355~359 (1992)
  3. J. M. Barbosa, "Minimal ruled submanifolds in spaces of constant curvature", Indiana Univ. Math. J, 33(4), pp.531~547 (1984)
  4. B. -Y. Chen, "Total Mean Curvature and Submanifolds of Finite Type" (1984), World Scientific
  5. B.-Y. Chen, "A report on submanifolds of finite type", Soochow J. Math, 22, pp.117~337 (1996)
  6. B. -Y. Chen, "On spectral decomposition of immersion of finite type", Bull. Austral. Math. Soc, 44(2) (1991)
  7. F. Dillen, "Ruled submanifolds of finite type", Proc. Amer. Math. Soc, 114(3), pp.795~798 (1992)
  8. F. Dillen, "On the Gauss map of surfaces of revolution", Bull. Inst. Math. Acad. Sinica, 18(3), pp.239~246 (1990)
  9. D. -S. Kim, "On the Gauss map of quadric hypersurfaces", J. Korean Math. Soc, 31(3), pp.429~437 (1994)
  10. D. -S. Kim, "Space curves satisfying H = AH, Bull", Korean Math. Soc, 31(2), pp.193~200 (1994)
  11. ¨U. Lumiste, "Die n-dimensionalen Minimalfl¨achen mit eineer (n + 1)-dimensionalen asymtotischen Richitung im jeden Punkute", Tarrtu Riikl. ¨Ul. Toimetised, 62, pp.117~141 (1958)
  12. T. Takahashi, "Minimal immersions of Riemannian manifolds", J. Math. Soc. Japan, 18, pp.380~385 (1966)

관련 논문AI추천

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