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On Surfaces of Finite Chen — Type

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We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the Euclidean space E3 and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.

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References

  1. Chen, B.-Y.: Total mean Curvature and Submanifolds of Finite Type, World Scientific Publisher, 1984.

  2. Chen, B.-Y.: Surfaces of finite type in Euclidean 3-space, Bull. Soc. Math. Belg. Ser. B, 39 (1987), 243–254.

    MathSciNet  MATH  Google Scholar 

  3. Chen, B.-Y.: Some open problems and conjectures on submanifolds of finite type, Soochow J. Math., 17 (1991), 169–188.

    MathSciNet  MATH  Google Scholar 

  4. Chen, B.-Y.: A report on submanifolds of finite type, Soochow J. Math., 22 (1996), 117–337.

    MathSciNet  MATH  Google Scholar 

  5. Huck, H., Simon, U., Roitzsch, R., Vortisch, W., Waiden, R., Wegner, B., Wendland, W.: Beweismethoden der Differentialgeometrie im Grossen, Lecture Notes in Mathematics. Vol. 335,1973.

  6. Stamatakis, S.: Der 2. Beltramische Operator der dritten Grundform einer Fläche des E3, Proceedings of the 4th International Congress of Geometry, Thessaloniki (1996), 392-396.

  7. Takahashi, T.: Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380–385.

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Correspondence to Stylianos Stamatakis.

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Stamatakis, S., Al-Zoubi, H. On Surfaces of Finite Chen — Type. Results. Math. 43, 181–190 (2003). https://doi.org/10.1007/BF03322734

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