Research Article
Year 2017,
Volume: 5 Issue: 2, 273 - 276, 30.03.2017
Abstract
In this paper, we obtain some results on the dimension of the isometry group of a Riemannian manifold. In specific dimensions, we give a range which the dimension of an isometry group can not be in. We also give necessary conditions for a manifold to have a free canonical action on some specific manifolds. We give a boundary of the dimension of the full isometry group if the dimension of a manifold is greater or equal to 4.
References
- Alexandrino, Marcos M., Bettiol, Renato G. Lie Groups and Geometric Aspects of Isometric Actions ,Springer International Publishing Switzerland, (2015).
- Fox, Ralph H., On topologies for function spaces, Bull. Amer. Math. Soc., 51 , 429-432, (1945).
- Ihrig, Edwin., The Size of Isometry Groups on Metric Spaces, J. Mathematical Analysis and Applications, 96, 447-453, (1983).
- Kadioglu H., Fisher R., Metric Structures on Fibered Manifolds Through Partitions of Unity, New Trends in Mathematical Sciences, 4(2), 266-272, (2016).
- Kadioglu H., Prolongations of Isometric Actions to Vector Bundles, Under Review, (2016).
- Kobayashi, S., Transformation groups in differential geometry, Ergeb. der Math. and ihrer Grenzgeb., (70,) Springer, Berlin (1972).
- Myers S. B. and Steenrod N.E., The Group of Isometries of a Riemannian Manifold, The Annals of Mathematics, 40, 2, 400-416, (1939).
- Mann, L. N., Gaps in Dimensions of Isometry Groups of Riemannian Manifolds, J. Differential Geometry, 11, 293-298, (1976).
- Postnikov, M. M., Geometry VI: Riemannian Geometry, Springer Science and Business Media, (2001).
- Wakakuwa, H., On n-dimensional Riemannian Spaces admitting some groups of Motions of order less than n(n-1)/2, Tohoku Math. J., 2(6), 121-134, (1954).
- Wang, H. C., Finsler Spaces with Completely Integrable Equations of Killing, J. London Math Soc., 22, 5-9, (1947).
Year 2017,
Volume: 5 Issue: 2, 273 - 276, 30.03.2017
Abstract
References
- Alexandrino, Marcos M., Bettiol, Renato G. Lie Groups and Geometric Aspects of Isometric Actions ,Springer International Publishing Switzerland, (2015).
- Fox, Ralph H., On topologies for function spaces, Bull. Amer. Math. Soc., 51 , 429-432, (1945).
- Ihrig, Edwin., The Size of Isometry Groups on Metric Spaces, J. Mathematical Analysis and Applications, 96, 447-453, (1983).
- Kadioglu H., Fisher R., Metric Structures on Fibered Manifolds Through Partitions of Unity, New Trends in Mathematical Sciences, 4(2), 266-272, (2016).
- Kadioglu H., Prolongations of Isometric Actions to Vector Bundles, Under Review, (2016).
- Kobayashi, S., Transformation groups in differential geometry, Ergeb. der Math. and ihrer Grenzgeb., (70,) Springer, Berlin (1972).
- Myers S. B. and Steenrod N.E., The Group of Isometries of a Riemannian Manifold, The Annals of Mathematics, 40, 2, 400-416, (1939).
- Mann, L. N., Gaps in Dimensions of Isometry Groups of Riemannian Manifolds, J. Differential Geometry, 11, 293-298, (1976).
- Postnikov, M. M., Geometry VI: Riemannian Geometry, Springer Science and Business Media, (2001).
- Wakakuwa, H., On n-dimensional Riemannian Spaces admitting some groups of Motions of order less than n(n-1)/2, Tohoku Math. J., 2(6), 121-134, (1954).
- Wang, H. C., Finsler Spaces with Completely Integrable Equations of Killing, J. London Math Soc., 22, 5-9, (1947).
There are 11 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | March 30, 2017 |
| Published in Issue | Year 2017 Volume: 5 Issue: 2 |
