Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces
Yıl 2019,
Cilt: 12 Sayı: 1, 116 - 125, 27.03.2019
Mehmet Gülbahar
,
Erol Kılıç
,
Sadık Keleş
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
Mehmet Gülbahar
,
Erol Kılıç
,
Sadık Keleş
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.