We all are familiar with the kind of differential geometry where some affine connection always exists to relate various tangent spaces distributed over the manifold, and from this connection two fundamental tensors, namely the Cartan's torsion and the Riemann-Christoffel curvature, arise.(adsbygoogle = window.adsbygoogle || []).push({});

Is it possible to have a differential manifold, where due to some topological anomaly, a connection cannot exist?

Of course there exists symplectic manifolds where no connection property is required.

But my question is related to the existence of non-metricity --- as in non-metric case, metric property id there but the connection is not metric. Similarly, can we have some property called non-connectivity where the affine connection is there but somehow it is lacking some fundamental connection requirements?

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

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

# Differential manifold without connection: Is it possible?

Loading...

Similar Threads for Differential manifold without |
---|

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 |

A Is tangent bundle TM the product manifold of M and T_pM? |

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