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Affine completeness and euclidean completeness

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Global Differential Geometry and Global Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1481))

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References

  1. E. Calabi, Hypersurfaces with Maximal Affinely Invariant area, Amer. J. Math. 104, 91–126, (1982).

    Article  MathSciNet  MATH  Google Scholar 

  2. S.Y. Cheng and S.T. Yau, Complete Affine Hypersurfaces, Part 1 The Completeness of Affine Metrics, Comm. Pure and Appl. Math. 39 (1986) 839–866.

    Article  MathSciNet  MATH  Google Scholar 

  3. S.S. Chern, Affine Minimal Hypersurfaces, Proc. Jap-U.S. Semin. Tokyo 1977, 17–30 (1978).

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  4. A. Schwenk and U. Simon, Hypersurfaces with Constant Equiaffine Mean Curvature. Arch. Math. Vol. 46 (1986), 85–90.

    Article  MathSciNet  MATH  Google Scholar 

  5. Li An-Min, Calabi Conjecture on Hyperbolic Affine Hyperspheres, Math. Z. 203, 483–491 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  6. Li An-Min, Calabi Conjecture on Hyperbolic Affine Hyperspheres (2), Preprint No. 248/1990, TU Berlin.

    Google Scholar 

  7. A. Martinez and F. Milán, On the Affine Bernstein Problem, Geom. Dedicata 37, No. 3, 295–302 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  8. K. Nomizu, On completeness in affine differential geometry, Geom. Ded. 20. 43–49 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Schneider, Zur affinen Differentialgeometrie im Großen I Math. Z. 101, 375–406 (1967).

    Article  MathSciNet  MATH  Google Scholar 

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Dirk Ferus Ulrich Pinkall Udo Simon Berd Wegner

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© 1991 Springer-Verlag

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An-Min, L. (1991). Affine completeness and euclidean completeness. 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/BFb0083635

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  • DOI: https://doi.org/10.1007/BFb0083635

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54728-0

  • Online ISBN: 978-3-540-46445-7

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