Tags » Geodesics

geodesics, covering map and its lift

Followings are given problems.

Let $f:(M,g)\rightarrow (N,h)$ a covering map that is a local isometry, and let $p\in M$. If $\gamma: \rightarrow N$ is a geodesic such that $\gamma(0)=f(p(0))$, then we can lift $\gamma$ to a geodesic $\tilde{\gamma}$:→M a geodesic with $\tilde{\gamma}(0)=p(0)$ … 45 more words

geodesics, covering map and its lift

Followings are given problems.

Let $f:(M,g)\rightarrow (N,h)$ a covering map that is a local isometry, and let $p\in M$. If $\gamma: \rightarrow N$ is a geodesic such that $\gamma(0)=f(p)$, then we can lift $\gamma$ to a geodesic $\tilde{\gamma}$:→M a geodesic with $\tilde{\gamma}(0)=p$ 24 more words