Timeline for When is a simply connected Lie group with an invariant metric of positive sectional curvature compact?

10 events

when toggle format	what		by	license	comment
Mar 13, 2018 at 1:09	history	edited	j.c.	CC BY-SA 3.0	attempt at fixing grammar
S Mar 12, 2018 at 23:50	history	suggested	Ali Taghavi		I add two tags.
Mar 12, 2018 at 19:41	review	Suggested edits
S Mar 12, 2018 at 23:50
Aug 30, 2017 at 0:58	comment	added	L.F. Cavenaghi		It could happen the manifold be like a paraboloid that is not compact and the curvature even positive approaches widely of zero.
Aug 30, 2017 at 0:57	comment	added	L.F. Cavenaghi		The answer I was expecting was given by @NateEldredge, I was not sure about it and as you claimed it trivially follows. Thanks.
Aug 30, 2017 at 0:32	comment	added	Nate Eldredge		In particular, the Ricci curvature is positive at each point. You're worried it might not be uniformly bounded away from 0? But by the invariance of the metric, the Ricci curvature is "constant", i.e. if $\mathrm{Ric} \ge k > 0$ at one point, then the same is true everywhere.
Aug 30, 2017 at 0:32	comment	added	Tim Carson		In particular the lie group structure means that positive sectional curvature implies strictly positive sectional curvature.
Aug 30, 2017 at 0:29	comment	added	John Pardon		Positive sectional curvature implies positive Ricci curvature, so you're done by Bonnet--Myers (and simple connectivity is irrelevant). But you've included this argument in the question statement, so what are you asking?
Aug 30, 2017 at 0:16	history	edited	L.F. Cavenaghi	CC BY-SA 3.0	deleted 1 character in body
Aug 30, 2017 at 0:10	history	asked	L.F. Cavenaghi	CC BY-SA 3.0