I am trying to understand differentiable manifolds and have some questions about this topic:(adsbygoogle = window.adsbygoogle || []).push({});

We can think of a circle as a 1-dim manifold and make it into a differentiable manifold by defining a suitable atlas. For example two open sets and stereographic projection etc. would be the choice.But in anyway we have to begin with a coordinate system (and generally it is cartesian coordinate system ) Is there a way to assign charts to a circle without referring to cartesian coord.? And isn't that unusual to be able to define differentiablity without using metric, norm..

(I know my question looks silly , but I hope the replies will make some points more clear for me)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Understand differentiable manifolds

Loading...

Similar Threads for Understand differentiable manifolds |
---|

A How to calculate the second fundamental form of a submanifold? |

I Diffeomorphism invariance and contracted Bianchi identity |

A Smoothness of multivariable function |

A Smooth extension on manifolds |

I Is my understanding correct? |

**Physics Forums | Science Articles, Homework Help, Discussion**