Research Article
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Year 2024, Volume: 17 Issue: 2, 551 - 558, 27.10.2024
https://doi.org/10.36890/iejg.1405824

Abstract

References

  • [1] Abedi, H., Kashani, S. M. B.: Cohomogeneity one Riemannian manifolds of constant positive curvature. Journal of the Korean Math. Soci. 44, 799-807 (2007). https://doi.org/10.1016/j.difgeo.2007.06.006
  • [2] Ahmadi, P., Kashani, S. M. B.: Cohomogeneity one Anti De Sitter space H3 1 . Bulletin of the Irannian Math. Soc. 35, 221-233 (2009).
  • [3] Ahmadi, P.: Cohomogeneity one Lorentzian space forms: Minkowski, de Sitter and anti de Sitter spaces. Lap Lambert Academic Publishing (2011).
  • [4] Alekseevsky, D. V.: Homogeneous Lorentzian manifolds of a semisimple group. Journal of Geomerty and Physics. 62, 631-645 (2012). https://doi.org/10.48550/arxiv.1101.3093
  • [5] Bredon, G. E.: Introdution to compact transformation groups. Acad. Press. New york, London (1972).
  • [6] Berndt, J., Bruk, M.: Cohomogeneity one actions on hyperbolic spaces. Journal fur die Reine und Angewandte Mathematik. 209-235 (2001). https://doi.org/10.1515/crll.2001.093
  • [7] Brendt, J., Console, S., Olmos, C.: Submanifolds and holonomy, Chapman and Hall/CRS. London, New york (2003).
  • [8] Calvaruso, G., Lopez, C.: Pseudo-Riemannian homogeneous structures. Springer Cham, Switzerland (2019).
  • [9] Dadok, J.: Polar coordinates induced by actions of compact Lie groups. Trans. Amer. Math. Soc. 228, 125-137 (1985).
  • [10] Diaz-Ramos, J. C., Kashani, S. M. B., Vanaei, M. J.: Cohomogeneity one actions on anti de Sitter spacetimes. Preprint arxiv:1609.05644[math.DG]. https://doi.org/10.48550/arXiv.1609.05644
  • [11] Eberlin, P., O’Neil, B.:Visibility manifolds. Pasific J. Math. 46, 45-109 (1973).
  • [12] Kobayashi, S.: Homogeneous Riemannian manifolds of negative curuature. Tohoku Math. J. 14, 413-415 (1962). https://doi.org/10.2748/tmj/1178244077
  • [13] Kollros, A.: A classification of hyperpolar and cohomogeneity one actions. Trans. Amer. Math. Soc. 354, 571-612 (2002).
  • [14] Mirzaie, R.: Topological properties of some flat Lorentzian manifolds of low cohomogeneity. Hiroshima Math. J. 44, 267-274 (2014). https://doi.org/10.32917/hmj/1419619747
  • [15] Mirzaie, R.: Orbit space of cohomogeneity two flat Riemannian manifolds. Balkan Journal of Geometry and Its Applications. 2, 25-33 (2018).
  • [16] Mostert, P.: On a compact Lie group action on manifolds. Ann. Math. 65, 447-455 (1957).
  • [17] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. New York (1983).
  • [18] Patrangenaru, V.: Lorentzian manifolds with the three largest degrees of symmetry. Geometria Dedicata. 102, 25-33 (2003). https://doi.org/10.1023/b:geom.0000006588.95481.1c
  • [19] Podesta, F., Spiro, A.: Some topological properties of cohomogeneity one manifolds with negative curvature. Ann. Glob. Anal. Geom. 14, 69-79 (1966). https://doi.org/10.1007/bf00128196
  • [20] Podesta, F., Verdiani, L.: Positively curved 7-dimensional manifolds. Quart. J. Math. Oxford Ser. 50, 497-504 (1999). https://doi.org/10.48550/arxiv.dg-ga/9712002
  • [21] Searle, C.: Cohomogeneity and positive curvature in low dimensions. Math. Z. 214, 491-498 (1993).
  • [22] Scala, A. J. Di., Olmos, C.: The geometry of homogeneous submanifolds of hyperbolic space. Math. Z. 237, 199-209 (2001). https://doi.org/10.1007/PL00004860
  • [23] Szeghy, D.: Isometric actions of compact connected Lie groups on globally hyperbolic Lorentz manifolds. Publ. Math. Debrecen. 71, 229-243 (2007). https://doi.org/10.5486/pmd.2007.3730
  • [24] Wolf, J. A.: Flat homogeneous pseudo-Riemannian manifolds. Geometria Dedicata. 57, 111-120 (1995). https://doi.org/10.1007/BF01264064
  • [25] Wolf, J. A.: Spaces of constant curvature. McGraw-Hill, New York (1967).

Lorentzian G-manifolds of Constant Positive Curvature

Year 2024, Volume: 17 Issue: 2, 551 - 558, 27.10.2024
https://doi.org/10.36890/iejg.1405824

Abstract

We study the orbits arising from isometric actions of connected Lie groups on Lorentzian manifolds
with constant positive curvature.

References

  • [1] Abedi, H., Kashani, S. M. B.: Cohomogeneity one Riemannian manifolds of constant positive curvature. Journal of the Korean Math. Soci. 44, 799-807 (2007). https://doi.org/10.1016/j.difgeo.2007.06.006
  • [2] Ahmadi, P., Kashani, S. M. B.: Cohomogeneity one Anti De Sitter space H3 1 . Bulletin of the Irannian Math. Soc. 35, 221-233 (2009).
  • [3] Ahmadi, P.: Cohomogeneity one Lorentzian space forms: Minkowski, de Sitter and anti de Sitter spaces. Lap Lambert Academic Publishing (2011).
  • [4] Alekseevsky, D. V.: Homogeneous Lorentzian manifolds of a semisimple group. Journal of Geomerty and Physics. 62, 631-645 (2012). https://doi.org/10.48550/arxiv.1101.3093
  • [5] Bredon, G. E.: Introdution to compact transformation groups. Acad. Press. New york, London (1972).
  • [6] Berndt, J., Bruk, M.: Cohomogeneity one actions on hyperbolic spaces. Journal fur die Reine und Angewandte Mathematik. 209-235 (2001). https://doi.org/10.1515/crll.2001.093
  • [7] Brendt, J., Console, S., Olmos, C.: Submanifolds and holonomy, Chapman and Hall/CRS. London, New york (2003).
  • [8] Calvaruso, G., Lopez, C.: Pseudo-Riemannian homogeneous structures. Springer Cham, Switzerland (2019).
  • [9] Dadok, J.: Polar coordinates induced by actions of compact Lie groups. Trans. Amer. Math. Soc. 228, 125-137 (1985).
  • [10] Diaz-Ramos, J. C., Kashani, S. M. B., Vanaei, M. J.: Cohomogeneity one actions on anti de Sitter spacetimes. Preprint arxiv:1609.05644[math.DG]. https://doi.org/10.48550/arXiv.1609.05644
  • [11] Eberlin, P., O’Neil, B.:Visibility manifolds. Pasific J. Math. 46, 45-109 (1973).
  • [12] Kobayashi, S.: Homogeneous Riemannian manifolds of negative curuature. Tohoku Math. J. 14, 413-415 (1962). https://doi.org/10.2748/tmj/1178244077
  • [13] Kollros, A.: A classification of hyperpolar and cohomogeneity one actions. Trans. Amer. Math. Soc. 354, 571-612 (2002).
  • [14] Mirzaie, R.: Topological properties of some flat Lorentzian manifolds of low cohomogeneity. Hiroshima Math. J. 44, 267-274 (2014). https://doi.org/10.32917/hmj/1419619747
  • [15] Mirzaie, R.: Orbit space of cohomogeneity two flat Riemannian manifolds. Balkan Journal of Geometry and Its Applications. 2, 25-33 (2018).
  • [16] Mostert, P.: On a compact Lie group action on manifolds. Ann. Math. 65, 447-455 (1957).
  • [17] O’Neill, B.: Semi-Riemannian geometry with applications to relativity. Academic Press. New York (1983).
  • [18] Patrangenaru, V.: Lorentzian manifolds with the three largest degrees of symmetry. Geometria Dedicata. 102, 25-33 (2003). https://doi.org/10.1023/b:geom.0000006588.95481.1c
  • [19] Podesta, F., Spiro, A.: Some topological properties of cohomogeneity one manifolds with negative curvature. Ann. Glob. Anal. Geom. 14, 69-79 (1966). https://doi.org/10.1007/bf00128196
  • [20] Podesta, F., Verdiani, L.: Positively curved 7-dimensional manifolds. Quart. J. Math. Oxford Ser. 50, 497-504 (1999). https://doi.org/10.48550/arxiv.dg-ga/9712002
  • [21] Searle, C.: Cohomogeneity and positive curvature in low dimensions. Math. Z. 214, 491-498 (1993).
  • [22] Scala, A. J. Di., Olmos, C.: The geometry of homogeneous submanifolds of hyperbolic space. Math. Z. 237, 199-209 (2001). https://doi.org/10.1007/PL00004860
  • [23] Szeghy, D.: Isometric actions of compact connected Lie groups on globally hyperbolic Lorentz manifolds. Publ. Math. Debrecen. 71, 229-243 (2007). https://doi.org/10.5486/pmd.2007.3730
  • [24] Wolf, J. A.: Flat homogeneous pseudo-Riemannian manifolds. Geometria Dedicata. 57, 111-120 (1995). https://doi.org/10.1007/BF01264064
  • [25] Wolf, J. A.: Spaces of constant curvature. McGraw-Hill, New York (1967).
There are 25 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Reza Mirzaie

Jafar Ebrahimi

Early Pub Date September 29, 2024
Publication Date October 27, 2024
Submission Date December 16, 2023
Acceptance Date September 27, 2024
Published in Issue Year 2024 Volume: 17 Issue: 2

Cite

APA Mirzaie, R., & Ebrahimi, J. (2024). Lorentzian G-manifolds of Constant Positive Curvature. International Electronic Journal of Geometry, 17(2), 551-558. https://doi.org/10.36890/iejg.1405824
AMA Mirzaie R, Ebrahimi J. Lorentzian G-manifolds of Constant Positive Curvature. Int. Electron. J. Geom. October 2024;17(2):551-558. doi:10.36890/iejg.1405824
Chicago Mirzaie, Reza, and Jafar Ebrahimi. “Lorentzian G-Manifolds of Constant Positive Curvature”. International Electronic Journal of Geometry 17, no. 2 (October 2024): 551-58. https://doi.org/10.36890/iejg.1405824.
EndNote Mirzaie R, Ebrahimi J (October 1, 2024) Lorentzian G-manifolds of Constant Positive Curvature. International Electronic Journal of Geometry 17 2 551–558.
IEEE R. Mirzaie and J. Ebrahimi, “Lorentzian G-manifolds of Constant Positive Curvature”, Int. Electron. J. Geom., vol. 17, no. 2, pp. 551–558, 2024, doi: 10.36890/iejg.1405824.
ISNAD Mirzaie, Reza - Ebrahimi, Jafar. “Lorentzian G-Manifolds of Constant Positive Curvature”. International Electronic Journal of Geometry 17/2 (October 2024), 551-558. https://doi.org/10.36890/iejg.1405824.
JAMA Mirzaie R, Ebrahimi J. Lorentzian G-manifolds of Constant Positive Curvature. Int. Electron. J. Geom. 2024;17:551–558.
MLA Mirzaie, Reza and Jafar Ebrahimi. “Lorentzian G-Manifolds of Constant Positive Curvature”. International Electronic Journal of Geometry, vol. 17, no. 2, 2024, pp. 551-8, doi:10.36890/iejg.1405824.
Vancouver Mirzaie R, Ebrahimi J. Lorentzian G-manifolds of Constant Positive Curvature. Int. Electron. J. Geom. 2024;17(2):551-8.