Araştırma Makalesi
BibTex RIS Kaynak Göster

Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces

Yıl 2019, Cilt: 12 Sayı: 1, 116 - 125, 27.03.2019
https://doi.org/10.36890/iejg.545856

Öz

Riemannian submersions between Lie groups and Riemannian homogeneous spaces are
investigated. With the help of connections, some characterizations dealing these spaces are
obtained.

Kaynakça

  • [1] Agricola, I., Ferreira, A. C., Tangent Lie groups are Riemannian naturally reductive spaces. Adv. in Appl. Clifford Algebras 27 (2017), 895-911.
  • [2] Arvanitogeorgos, A., An introduction to Lie groups and the geometry of homogeneous spaces. American Mathematical Soc. 22, 2003.
  • [3] Arvanitoyeorgos, A., Lie transformation groups and geometry. In Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization (pp. 11-35). Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 2008.
  • [4] Berdinsky, D. A., Taimanov, I. A., Surfaces in three-dimensional Lie groups. Siberian Math. J. 46(6) (2005), 1005–1019.
  • [5] Besse, A. L., Einstein manifolds. Springer Science, Business Media, 2007.
  • [6] Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian submersions and related topics. World Scientific Company, 2004.
  • [7] Fegan, H. D., Introduction to compact Lie groups. Vol. 13, World Scientific Publishing Company, 1991.
  • [8] Ferus, D., Symmetric submanifolds of Euclidean space. Mathematische Annalen 247(1) (1980), 81-93.
  • [9] Guijarro, L., Walschap, G., When is a Riemannian submersion homogeneous?. Geometriae Dedicata 125(1) (2007), 47-52.
  • [10] Gülbahar, M., Eken Meriç S., Kılıç, E., Sharp inequalities involving the Ricci curvature for Riemannian submersions. Kragujevac J. Math. 42(2) (2017), 279-293. [11] Hsiang, W.Y., Lawson Jr, H. B., Minimal submanifolds of low cohomogeneity. J. Differential Geom. 5(1-2) (1971), 1-38.
  • [12] Kirillov, A. A., Elements of the theory of representations. Springer-Verlag, Berlin, Heidelberg, New York 1976.
  • [13] Kobayashi, S., Submersions of CR-submanifolds. Tohoku Math. J. 89 (1987), 95-100.
  • [14] Megia, I. S. M., Which spheres admit a topological group structure. Rev. R. Acad. Cienc. Exactas Fıs. Quım. Nat. Zaragoza 62 (2007), 75-79.
  • [15] O’Neill, B., Semi-Riemannian geometry with applications to relativity. Academic press, United Kingdom (1983).
  • [16] Pro, C., Wilhelm, F., Flats and submersions in non-negative curvature. Geometriae Dedicata 161(1) (2012), 109-118.
  • [17] Ranjan, A., Riemannian submersions of compact simple Lie groups with connected totally geodesic fibres. Mathematische Zeitschrift 191(2) (1986), 239-246.
  • [18] Sahin, B., Riemannian submersions, Riemannian maps in Hermitian geometry and their applications. Academic Press 2017.
  • [19] Sepanski, M. R., Compact lie groups. Springer Science, Business Media, 2007.
  • [20] Tapp, K., Flats in Riemannian submersions from Lie groups. Asian J. of Math. 13(4) (2009), 459-464.
Yıl 2019, Cilt: 12 Sayı: 1, 116 - 125, 27.03.2019
https://doi.org/10.36890/iejg.545856

Öz

Kaynakça

  • [1] Agricola, I., Ferreira, A. C., Tangent Lie groups are Riemannian naturally reductive spaces. Adv. in Appl. Clifford Algebras 27 (2017), 895-911.
  • [2] Arvanitogeorgos, A., An introduction to Lie groups and the geometry of homogeneous spaces. American Mathematical Soc. 22, 2003.
  • [3] Arvanitoyeorgos, A., Lie transformation groups and geometry. In Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization (pp. 11-35). Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 2008.
  • [4] Berdinsky, D. A., Taimanov, I. A., Surfaces in three-dimensional Lie groups. Siberian Math. J. 46(6) (2005), 1005–1019.
  • [5] Besse, A. L., Einstein manifolds. Springer Science, Business Media, 2007.
  • [6] Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian submersions and related topics. World Scientific Company, 2004.
  • [7] Fegan, H. D., Introduction to compact Lie groups. Vol. 13, World Scientific Publishing Company, 1991.
  • [8] Ferus, D., Symmetric submanifolds of Euclidean space. Mathematische Annalen 247(1) (1980), 81-93.
  • [9] Guijarro, L., Walschap, G., When is a Riemannian submersion homogeneous?. Geometriae Dedicata 125(1) (2007), 47-52.
  • [10] Gülbahar, M., Eken Meriç S., Kılıç, E., Sharp inequalities involving the Ricci curvature for Riemannian submersions. Kragujevac J. Math. 42(2) (2017), 279-293. [11] Hsiang, W.Y., Lawson Jr, H. B., Minimal submanifolds of low cohomogeneity. J. Differential Geom. 5(1-2) (1971), 1-38.
  • [12] Kirillov, A. A., Elements of the theory of representations. Springer-Verlag, Berlin, Heidelberg, New York 1976.
  • [13] Kobayashi, S., Submersions of CR-submanifolds. Tohoku Math. J. 89 (1987), 95-100.
  • [14] Megia, I. S. M., Which spheres admit a topological group structure. Rev. R. Acad. Cienc. Exactas Fıs. Quım. Nat. Zaragoza 62 (2007), 75-79.
  • [15] O’Neill, B., Semi-Riemannian geometry with applications to relativity. Academic press, United Kingdom (1983).
  • [16] Pro, C., Wilhelm, F., Flats and submersions in non-negative curvature. Geometriae Dedicata 161(1) (2012), 109-118.
  • [17] Ranjan, A., Riemannian submersions of compact simple Lie groups with connected totally geodesic fibres. Mathematische Zeitschrift 191(2) (1986), 239-246.
  • [18] Sahin, B., Riemannian submersions, Riemannian maps in Hermitian geometry and their applications. Academic Press 2017.
  • [19] Sepanski, M. R., Compact lie groups. Springer Science, Business Media, 2007.
  • [20] Tapp, K., Flats in Riemannian submersions from Lie groups. Asian J. of Math. 13(4) (2009), 459-464.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Mehmet Gülbahar

Erol Kılıç

Sadık Keleş

Yayımlanma Tarihi 27 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 12 Sayı: 1

Kaynak Göster

APA Gülbahar, M., Kılıç, E., & Keleş, S. (2019). Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces. International Electronic Journal of Geometry, 12(1), 116-125. https://doi.org/10.36890/iejg.545856
AMA Gülbahar M, Kılıç E, Keleş S. Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces. Int. Electron. J. Geom. Mart 2019;12(1):116-125. doi:10.36890/iejg.545856
Chicago Gülbahar, Mehmet, Erol Kılıç, ve Sadık Keleş. “Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces”. International Electronic Journal of Geometry 12, sy. 1 (Mart 2019): 116-25. https://doi.org/10.36890/iejg.545856.
EndNote Gülbahar M, Kılıç E, Keleş S (01 Mart 2019) Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces. International Electronic Journal of Geometry 12 1 116–125.
IEEE M. Gülbahar, E. Kılıç, ve S. Keleş, “Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces”, Int. Electron. J. Geom., c. 12, sy. 1, ss. 116–125, 2019, doi: 10.36890/iejg.545856.
ISNAD Gülbahar, Mehmet vd. “Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces”. International Electronic Journal of Geometry 12/1 (Mart 2019), 116-125. https://doi.org/10.36890/iejg.545856.
JAMA Gülbahar M, Kılıç E, Keleş S. Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces. Int. Electron. J. Geom. 2019;12:116–125.
MLA Gülbahar, Mehmet vd. “Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces”. International Electronic Journal of Geometry, c. 12, sy. 1, 2019, ss. 116-25, doi:10.36890/iejg.545856.
Vancouver Gülbahar M, Kılıç E, Keleş S. Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces. Int. Electron. J. Geom. 2019;12(1):116-25.