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Indefinite extrinsic symmetric spaces

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Abstract

We extend Ferus’ characterization of extrinsic symmetric spaces to ambient spaces with indefinite inner products.

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References

  1. Berndt J., Console S., Olmos C.: Submanifolds and Holonomy. Research Notes in Mathematics. Chapman & Hall/CRC, Boca Raton (2003)

    Book  Google Scholar 

  2. Cahen M., Parker M.: Pseudo-Riemannian Symmetric Spaces. Memoirs Am. Math. Soc. 229, 1–108 (1980)

    MathSciNet  Google Scholar 

  3. Eschenburg J.-H., Heintze E.: Extrinsic symmetric spaces and orbits of s-representations. manuscr. math. 88, 517–524 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ferus D.: Immersions with parallel second fundamental form. J. Differ. Geom. 5, 333–340 (1974)

    Google Scholar 

  5. Ferus D.: Symmetric submanifolds of euclidean space. Math. Ann. 247, 81–93 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kath, I.: Extrinsic symmetric spaces I. arXiv:0809.4713, to appear in J. Reine u. Ang. Math.

  7. Kim, J.R.: Indefinite extrinsic symmetric spaces. Thesis Augsburg (2005)

  8. Naitoh H.: Pseudo-Riemannian symmetric R-spaces. Osaka J. Math. 21, 733–764 (1984)

    MATH  MathSciNet  Google Scholar 

  9. Strübing W.: Symmetric submanifolds of Riemannian manifolds. Math. Ann. 245, 37–44 (1979)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to J. -H. Eschenburg.

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J. R. Kim would like to thank DFG for financial support in the framework of the Graduiertenkolleg “Nichtlineare Probleme in Analysis, Geometrie und Physik”.

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Kim, J.R., Eschenburg, J.H. Indefinite extrinsic symmetric spaces. manuscripta math. 135, 203–214 (2011). https://doi.org/10.1007/s00229-011-0441-1

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  • DOI: https://doi.org/10.1007/s00229-011-0441-1

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