Abstract
In this paper, we obtain some results on the dimension of the isometry group of a Riemannian manifold. In specic 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 specic 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.
Keywords
Mathematics
Isometry (Riemannian geometry)
Dimension (graph theory)
Pure mathematics
Riemannian manifold
Isometry group
Group (periodic table)
Pseudo-Riemannian manifold
Manifold (fluid mechanics)
Mathematical analysis
Ricci curvature
Physics
Geometry
Subject Areas
Geometric Analysis and Curvature Flows
·Applied Mathematics ·Physical Sciences
Topological and Geometric Data Analysis
·Computational Theory and Mathematics ·Physical Sciences
Advanced Differential Geometry Research
·Astronomy and Astrophysics ·Physical Sciences