Timeline for Length of non-horizontal curve

10 events

when toggle format	what		by	license	comment
Feb 19, 2015 at 5:16	vote	accept	Nikita Evseev
Feb 18, 2015 at 12:26	history	edited	Robert Bryant	CC BY-SA 3.0	fixed grammar and improved formatting
Feb 18, 2015 at 9:46	comment	added	Robert Bryant		@NikitaEvseev: Yes. It's an unfortunate convention in Riemannian geometry that the underlying quadratic form $g$ on $M$ is called a 'Riemannian metric', even though it is not a 'metric' in the sense of metric spaces. Of course, it does define a metric $\delta_g:M\times M\to [0,\infty)$, where $\delta_g(x,y)$ is the infimum of the $g$-lengths of piecewise $C^1$ curves joining $x$ to $y$ (when $M$ is connected).
Feb 18, 2015 at 5:41	comment	added	Nikita Evseev		In "Second", is $g$ a quadratic form (not metric) ?
Feb 18, 2015 at 3:23	history	edited	Robert Bryant	CC BY-SA 3.0	Added a proof of the desired statement.
Feb 18, 2015 at 2:46	history	undeleted	Robert Bryant
Feb 17, 2015 at 9:38	history	deleted	Robert Bryant		via Vote
Feb 17, 2015 at 9:38	history	edited	Robert Bryant	CC BY-SA 3.0	deleted 3106 characters in body
Feb 17, 2015 at 9:18	history	edited	Robert Bryant	CC BY-SA 3.0	Corrected some errors and gave more explicit examples
Feb 17, 2015 at 2:30	history	answered	Robert Bryant	CC BY-SA 3.0