Some remarks on G -actions with sections

Elisa Gage Casini

Rendiconti del Seminario Matematico della Università di Padova (2000)

  • Volume: 103, page 157-169
  • ISSN: 0041-8994

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Casini, Elisa Gage. "Some remarks on $G$-actions with sections." Rendiconti del Seminario Matematico della Università di Padova 103 (2000): 157-169. <http://eudml.org/doc/108517>.

@article{Casini2000,
author = {Casini, Elisa Gage},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {-orbit; set of regular points; totally geodesic submanifold; nonpositive sectional curvatures; variationally complete; principal orbits; Weyl chambers; Weyl group},
language = {eng},
pages = {157-169},
publisher = {Seminario Matematico of the University of Padua},
title = {Some remarks on $G$-actions with sections},
url = {http://eudml.org/doc/108517},
volume = {103},
year = {2000},
}

TY - JOUR
AU - Casini, Elisa Gage
TI - Some remarks on $G$-actions with sections
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2000
PB - Seminario Matematico of the University of Padua
VL - 103
SP - 157
EP - 169
LA - eng
KW - -orbit; set of regular points; totally geodesic submanifold; nonpositive sectional curvatures; variationally complete; principal orbits; Weyl chambers; Weyl group
UR - http://eudml.org/doc/108517
ER -

References

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  1. [1] A. Alekseevsky - D. Alekseevsky, Asystatic G-manifolds, Proceedings of the workshop on Differential Geometry and Topology, Ed. R. Caddeo and F. Tricerri, World Scientific1993. Zbl0914.57023MR1339285
  2. [2] R. Bott, An application of the Morse theory to the topology of Lie groups, Bull. Soc. Math. Franc., 84 (1956), pp. 251-281. Zbl0073.40001MR87035
  3. [3] R. Bott - H. Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. Math., 80 (1958), pp. 964-1029. Zbl0101.39702MR105694
  4. [4] G.E. Bredon, Introduction to compact transformation groups, Academic Press, New York and London, 1972. Zbl0246.57017MR413144
  5. [5] L. Conlon, Variational completeness and K-transversal domains, J. Diff. Geom., 5 (1971), pp. 135-147. Zbl0213.48602MR295252
  6. [6] M.P. D, Geometria Riemanniana, Projeto Euclides, IMPA, Rio de Janeiro (1979). Zbl0505.53001
  7. [7] E. Heintze - R. Palais - L. Terng - G. Thorgbergsson, Hyperpolar actions and k-flat homogeneous spaces, Jour. Reine Angew. Math., 454 (1994), pp. 163-179. Zbl0804.53074MR1288683
  8. [8] S. Kobayashi - K. Nomizu, Foundations of Differential Geometry, vol. 1, Interscience publishers (1963). Zbl0119.37502MR152974
  9. [9] R.S. Palais - CH. L. TERNG, General theory of canonical forms, Trans. Am. Math. Soc., 300 (1987), pp. 771-789. Zbl0652.57023MR876478
  10. [10] R.S. Palais - Ch L. Terng, Critical Point Theory and Submanifold Geometry, LNM1353, Springer Verlag (1988). Zbl0658.49001MR972503
  11. [11] J. Szenthe, On the cut locus of a principal orbit in a Riemannian manifold of non-positive sectional curvature, Ann. Univ. Sci. Budapest. Eotvos. Sect. Math., 24 (1981), pp. 227-240. Zbl0484.53037MR878229
  12. [12] J. Szenthe, Orthogonally transversal submanifolds and the generalizations of the Weyl group, Per. Math. Hung., 15 (1984), pp. 281-299. Zbl0583.53035MR782429

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