# Tag Info

1 vote

### Can the exponential map be used to define geodesics (and hence, generalisations of geodesics)?

Let’s define $\gamma:\mathbb{R}\to M$ as a $\sigma$-geodesic iff for any $a,b,c\in\mathbb{R}$, there are vectors $v,w$ in the tangent space at $\gamma(a)$ with $$\sigma_{\gamma(a)}(v)=\gamma(b)$$ \...
• 18k