Advanced search
Publication Cover
Cogent Mathematics & Statistics Volume 5, 2018 - Issue 1
Submit an article Journal homepage
383
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Universally polar cohomogeneity two Riemannian manifolds of constant negative curvature

M. HeidariDepartment of Mathematics, Faculty of Science, Imam Khomeini International University (IKIU), Qazvin, IranView further author information
&
R. MirzaieDepartment of Mathematics, Faculty of Science, Imam Khomeini International University (IKIU), Qazvin, IranCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-9480-0222View further author information
ORCID Icon |
Hari M. SrivastavaDepartment of Mathematics and Statistics, University of Victoria, CanadaView further author information
(Reviewing editor)
Article: 1523516 | Received 24 Jan 2018, Accepted 03 Sep 2018, Published online: 14 Nov 2018

References

  • Alekseevsky, A., & Alekseevsky, D. (1993). Riemannian G-manifolds with one dimensional orbit space. Annals of Global Analysis and Geometry, 11, 197–211.
  • Berndt, J.(2011). Polar actions on symmetric spaces. Proceedings of The Fifteenth International Workshop on Diff. Geom (Vol. 15, pp. 1–10).
  • Bredon, G. E. (1972). Introduction to compact transformation groups. New York, London: Academic Press.
  • Dadok, J. (1985). Polar coordinates induced by actions of compact Lie groups. Transactions Amer Mathematical Social, 288, 125–137. doi:10.1090/S0002-9947-1985-0773051-1
  • Di Scala, A. J., & Olmos, C. (2001). The geometry of homogeneous submanifolds of hyperbolic space. Mathematical Z, 237, 199–209. doi:10.1007/PL00004860
  • Diaz-Ramos, J. C., & Kollross, A. (2011). Polar actions with a fixed point. Differential Geometry and Its Applications, 29, 20–25. doi:10.1016/j.difgeo.2011.01.001
  • Diaz-Ramos, J. C., Sanchez, M. Romero, A. (2013). Recent trends in lorentzian geometry. Springer Proceedings in Mathematics & Statistics. doi:10.1007/978-1-4614-4897-6-14.
  • Do Carmo, M. P. (1992). Riemannian geometry. Boston, MA: Birkhauser Boston, Inc.
  • Eberlein, P., & O’Neil, B. (1973). Visibility manifolds. Pasific Journal Mathematical, 46, 45–109. doi:10.2140/pjm.1973.46.45
  • Heidari, M., & Mirzaie, R. (2018). Polarity of cohomogeneity two actions on negatively curved space forms. To Appear in the Bulletin of the Korean Mathematical Social, (vol. 55, pp.1433-1440).
  • Heintze, E., Palais, R. S., Terng, C.-L., & Thorbergsson, G. (1995). Hyperpolar actions on symmetric spaces. Geometry, Topology, and physics, Conf. proc. Lecture Note Geom. Topology, IV (pp. 214–245). Cambridge, MA: Int. Press
  • Kobayashi, S. (1962). Homogeneous Riemannian manifolds of negative curvature. Tohoku Mathematical Journal, 14, 413–415. doi:10.2748/tmj/1178244077
  • Kollross, A. (2007). Polar actions on symmetric spaces. Journal of Differential Geometry, 77, 425–482. doi:10.4310/jdg/1193074901
  • Mirzaie, R. (2009). On negatively curved G-manifolds of low cohomogeneity. Hokkaido Mathematical Journal, 38, 797–803. doi:10.14492/hokmj/1258554244
  • Mirzaie, R. (2011a). On orbits of isometric actions on flat Riemannian manifolds. Kyushu Journal Mathematical, 65, 383–393. doi:10.2206/kyushujm.65.383
  • Mirzaie, R. (2011b). On Riemannian manifolds of constant negative curvature. Journal Korean Mathematical Society, 48, 23–31. doi:10.4134/JKMS.2011.48.1.023
  • Mirzaie, R., & Kashani, S. M. B. (2002). On cohomogeneity one flat Riemannian manifolds. Glasgow Mathematical Journal, 44, 185–190. doi:10.1017/S0017089502020189
  • Podesta, F., & Spiro, A. (1996). Some topological properties of cohomogeneity one Riemannian manifolds with negative curvature. Annals of Global Analysis and Geometry, 14, 69–79. doi:10.1007/BF00128196

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.