A differential geometric characterization of symmetric spaces of higher rank

Patrick Eberlein; Jens Heber

Publications Mathématiques de l'IHÉS (1990)

  • Volume: 71, page 33-44
  • ISSN: 0073-8301

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Eberlein, Patrick, and Jens Heber. "A differential geometric characterization of symmetric spaces of higher rank." Publications Mathématiques de l'IHÉS 71 (1990): 33-44. <http://eudml.org/doc/104066>.

@article{Eberlein1990,
author = {Eberlein, Patrick, Jens Heber},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {rank rigidity theorem; Hadamard manifold; isometry group; duality condition; Tits distance},
language = {eng},
pages = {33-44},
publisher = {Institut des Hautes Études Scientifiques},
title = {A differential geometric characterization of symmetric spaces of higher rank},
url = {http://eudml.org/doc/104066},
volume = {71},
year = {1990},
}

TY - JOUR
AU - Eberlein, Patrick
AU - Jens Heber
TI - A differential geometric characterization of symmetric spaces of higher rank
JO - Publications Mathématiques de l'IHÉS
PY - 1990
PB - Institut des Hautes Études Scientifiques
VL - 71
SP - 33
EP - 44
LA - eng
KW - rank rigidity theorem; Hadamard manifold; isometry group; duality condition; Tits distance
UR - http://eudml.org/doc/104066
ER -

References

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  1. [Ba1] W. BALLMANN, Axial isometries of manifolds of nonpositive curvature, Math. Ann., 259 (1982), 131-144. Zbl0487.53039MR83i:53068
  2. [Ba2] W. BALLMANN, Nonpositively curved manifolds of higher rank, Annals of Math., 122 (1985), 597-609. Zbl0585.53031MR87e:53059
  3. [BBE] W. BALLMANN, M. BRIN and P. EBERLEIN, Structure of manifolds of nonpositive curvature, I, Annals of Math., 122 (1985), 171-203. Zbl0589.53047MR87c:58092a
  4. [BBS] W. BALLMANN, M. BRIN and R. SPATZIER, Structure of manifolds of nonpositive curvature, II, Annals of Math., 122 (1985), 205-235. Zbl0598.53046MR87c:58092b
  5. [Be] M. BERGER, Sur les groupes d'holonomie homogène des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. France, 83 (1953), 279-330. Zbl0068.36002MR18,149a
  6. [BGS] W. BALLMANN, M. GROMOV and V. SCHROEDER, Manifolds of nonpositive curvature, Basel, Birkhäuser, 1985. Zbl0591.53001MR87h:53050
  7. [BO] R. BISHOP and O'NEILL, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49. Zbl0191.52002MR40 #4891
  8. [BS] K. BURNS and R. SPATZIER, Manifolds of nonpositive curvature and their buildings, Publ. Math. IHES, 65 (1987), 35-59. Zbl0643.53037MR88g:53050
  9. [E1] P. EBERLEIN, A differential geometric characterization of symmetric spaces of noncompact type and rank at least two, preprint, 1987. 
  10. [E2] P. EBERLEIN, Geodesic flows on negatively curved manifolds, I, Annals of Math., 95 (1972), 492-510. Zbl0217.47304MR46 #10024
  11. [E3] P. EBERLEIN, Isometry groups of simply connected manifolds of nonpositive curvature, II, Acta Math., 149 (1982), 41-69. Zbl0511.53048MR83m:53055
  12. [E4] P. EBERLEIN, Rigidity of lattices of nonpositive curvature, Erg. Th. Dynam. Sys., 3 (1983), 47-85. Zbl0521.53045MR86f:53049
  13. [E5] P. EBERLEIN, Symmetry diffeomorphism group of a manifold of nonpositive curvature, II, Indiana Univ. Math. Jour., 37 (1988), 735-752. Zbl0676.53054MR90e:53050
  14. [EO] P. EBERLEIN and B. O'NEILL, Visibility manifolds, Pacific J. Math., 46 (1973), 45-109. Zbl0264.53026MR49 #1421
  15. [GKM] D. GROMOLL, W. KLINGENBERG and W. MEYER, Riemannsche Geometrie im Grossen, Lecture Notes in Math., vol. 55, Berlin, Springer, 1968. Zbl0155.30701MR37 #4751

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