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.
Keywords
Isometry (Riemannian geometry)
Mathematics
Dimension (graph theory)
Riemannian manifold
Isometry group
Manifold (fluid mechanics)
Pure mathematics
Group (periodic table)
Pseudo-Riemannian manifold
Boundary (topology)
Mathematical analysis
Ricci curvature
Physics
Geometry
Curvature
Subject Areas
Geometric Analysis and Curvature Flows
·Applied Mathematics ·Physical Sciences
Advanced Neuroimaging Techniques and Applications
·Radiology, Nuclear Medicine and Imaging ·Health Sciences
Topological and Geometric Data Analysis
·Computational Theory and Mathematics ·Physical Sciences
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