# Definition:Isotropic Riemannian Manifold

Jump to navigation
Jump to search

This page has been identified as a candidate for refactoring of basic complexity.In particular: Create a structure where this and Definition:Riemannian Manifold Isotropic at Point are nested together in the same sense as Continuous and Continuous at Point, as they are both conceptually the same thing.Until this has been finished, please leave
`{{Refactor}}` in the code.
Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Refactor}}` from the code. |

## Definition

Let $\struct {M, g}$ be a Riemannian manifold.

Suppose $M$ is isotropic for all points $p \in M$.

Then $M$ is said to be **isotropic**.

## Sources

- 2018: John M. Lee:
*Introduction to Riemannian Manifolds*(2nd ed.) ... (previous) ... (next): $\S 3$: Model Riemannian Manifolds. Symmetries of Riemannian Manifolds