Rigidity of Rank-One Factors of Compact Symmetric Spaces

Andrew Clarke[1]

  • [1] Université de Nantes Laboratoire de Mathématiques Jean Leray 2, rue de la Houssinière - BP 92208 44322 Nantes Cedex 3 (France)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 2, page 491-509
  • ISSN: 0373-0956

Abstract

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We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

How to cite

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Clarke, Andrew. "Rigidity of Rank-One Factors of Compact Symmetric Spaces." Annales de l’institut Fourier 61.2 (2011): 491-509. <http://eudml.org/doc/219853>.

@article{Clarke2011,
abstract = {We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.},
affiliation = {Université de Nantes Laboratoire de Mathématiques Jean Leray 2, rue de la Houssinière - BP 92208 44322 Nantes Cedex 3 (France)},
author = {Clarke, Andrew},
journal = {Annales de l’institut Fourier},
keywords = {Minimal submanifolds; rigidity; symmetric spaces; minimal submanifold; totally geodesic submanifold; rank-one factor; symmetric space},
language = {eng},
number = {2},
pages = {491-509},
publisher = {Association des Annales de l’institut Fourier},
title = {Rigidity of Rank-One Factors of Compact Symmetric Spaces},
url = {http://eudml.org/doc/219853},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Clarke, Andrew
TI - Rigidity of Rank-One Factors of Compact Symmetric Spaces
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 2
SP - 491
EP - 509
AB - We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.
LA - eng
KW - Minimal submanifolds; rigidity; symmetric spaces; minimal submanifold; totally geodesic submanifold; rank-one factor; symmetric space
UR - http://eudml.org/doc/219853
ER -

References

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  8. H.B. Lawson Jr., Complete minimal surfaces in S 3 , Ann. of Math. 92 (1970), 335-374 Zbl0205.52001MR270280
  9. H.B. Lawson Jr., Rigidity theorems in rank-1 symmetric spaces, J. Diff. Geom. 4 (1970), 349-357 Zbl0199.56401MR267492
  10. N. Mok, Y.T. Siu, S.-K. Yeung, Geometric Superrigidity, J. Diff. Geom. 113 (1993), 57-83 Zbl0808.53043MR1223224
  11. L. Simon, Lecture Notes on Geometric Measure Theory, (1983), Australian National University 
  12. J. Simons, Minimal varieties in riemannian manifolds, Ann. Math. 88 (1968), 65-105 Zbl0181.49702MR233295
  13. D.Č. Thi, Minimal real currents on compact riemannian manifolds, Math. USSR Izv. 11 (1970), 807-820 Zbl0387.49042

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