Keywords
- Riemannian Manifold
- Minimal Surface
- Fundamental Form
- Finite Type
- Curvature Vector
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References
M. Barros and B.Y. Chen, Classification of stationary, 2-type surfaces of hyperspheres, C.R. Math. Rep. Acad. Sci. Canada, 7 (1985).
M. Barros and B.Y. Chen, Stationary 2-type surfaces in a hypersphere, to appear.
M. Barros, B.Y. Chen and O.J. Garay, Spherical finite type hypersurfaces, to appear.
B.Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973.
_____, Minimal surfaces with constant Gauss curvature, Proc. Amer. Math. Soc., 34 (1972), 504–508.
_____, Some conformal invariants of submanifolds and their applications, Boll. Un. Mat. Ital., 10 (1974), 380–385.
_____, On the total curvature of immersed manifolds; IV, Bull. Inst. Math. Acad. Sinica, 7 (1979), 301–311; _____; VI, ibid, 11 (1983), 309–328.
_____, Total Mean Curvature and Submanifolds of Finite Type, World Scientific, 1984.
_____, 2-type submanifolds and their applications, to appear.
_____, Finite Type Submanifolds and Generalizations, Quad. Sem. Top. Alg. Diff., Instituto "Castelnuovo", Rome, 1985.
S.S. Chern, M. doCarmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields, 1970, 59–75, Springer.
N. Ejiri, A counter example for Weiner's open question, Indiana Math. J., 31 (1982), 209–211.
J. Erbarcher, Reduction of the codimension of an isometric immersion, J. Diff. Geom., 5 (1971), 333–340.
F. John, Partial Differential Equations, Springer, 1971.
K. Kenmotsu, Minimal surfaces with constant curvature in 4-dimensional space forms, Proc. Amer. Math. Soc., 89 (1983), 133–138.
H.B. Lawson, Jr., Complete minimal surfaces in S3, Ann. of Math., 92 (1970), 335–374.
A. Ros, On spectral geometry of Kaehler submanifolds, J. Math. Soc. Japan, 36 (1984), 433–448.
_____, Eigenvalue inequalities for minimal submanifolds and P-manifolds, Math. Z. 187 (1984), 393–404.
T. Takahashi, Minimal immersionss of Riemannian manifolds, J. Math. Soc. Japan, 18 (1966), 380–385.
J.L. Weiner, On a problem of Chen, Willmore, et al., Indiana Math. J., 27 (1978), 19–35.
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© 1986 Springer-Verlag
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Barros, M., Chen, By. (1986). Finite type spherical submanifolds. In: Naveira, A.M., Ferrández, A., Mascaró, F. (eds) Differential Geometry Peñíscola 1985. Lecture Notes in Mathematics, vol 1209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076621
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DOI: https://doi.org/10.1007/BFb0076621
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