Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such ...
It is well known that odd and even dimensions work differently. Waves propagation in odd dimensions is unlike propagation in even dimensions. A parity operator is a rotation in even dimensions, ...
Let $\nabla_1$ and $\nabla_2$ be two affine connections of manifolds $M_1$ and $M_2$ and $\nabla$ induced connection on product $M_1\times M_2$. Prove the following: If $\gamma_1$, $\gamma_2$ are ...