Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ISOMETRIC IMMERSIONS OF MANIFOLDS INTO SPACE FORMS WITH THE SAME CONSTANT CURVATURES

  • Published : 2002.01.01
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Abstract

We study a unifying method to obtain nondegenerate isometric immersions of manifolds of constant sectional curvatures c with flat normal bundles into the space forms of curvature c for c= -1,0,1.

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References

  1. to appear in Mem. Amer. Math. Soc. The submanifold geometry of real Grassmannian systems M. Bruck,;X. Du;J. Park;C. L. Terng
  2. Bull. Soc. Math. Rrance v.47 Sur les varietes de courbure constante d'un espace euclidien ou non-euclidien E. Cartan
  3. Trans. Amer. math. Soc. v.2 Uber Flachen von konstanter Gausscher Krummung D. Hilbert
  4. Pacific Jour. Math. v.40 Isometric immersions of space forms in space forms J. Moore https://doi.org/10.2140/pjm.1972.40.157
  5. Boll. Soc. Brasil. Mat. v.16 Backlund's theorem for submanifolds of space forms and a generalized wave equation K. Tenenblat
  6. Ann. Math. v.111 Backlund's theorem for n-dimensional submanifolds of R²ⁿ-1 K. Tenenblat;C. L. Terng https://doi.org/10.2307/1971105
  7. Ann. Math. v.111 A. higher dimensional generalization of the sine-Gordon equation and its soliton theory C. L. Terng https://doi.org/10.2307/1971106
  8. Jour. Diff. Geom. v.45 Soliton equations and differential geometry