Timeline for Special Riemannian connections?

9 events

when toggle format	what		by	license	comment
Sep 1, 2014 at 18:21	vote	accept	Ramand
May 14, 2014 at 19:05	comment	added	Ramand		Thank you, I'm really Thankful. I appreciate your kind and soon respond.
May 14, 2014 at 18:23	comment	added	Robert Bryant		Yes, of course. Take any nontrivial, oriented, Euclidean $3$-plane bundle. For example, consider the canonical $3$-plane bundle over the Grassmannian $\mathrm{Gr}_3(\mathbb{R}^{n+3})$ of oriented $3$-planes in $\mathbb{R}^{n+3}$ for $n\ge 2$. Now endow it with the Lie algebra structure that I described above in my answer.
May 14, 2014 at 15:38	comment	added	Ramand		thank you Prof. Robert Bryant. Is there example of non-trivial bundle of Lie Algebras?
May 11, 2014 at 18:10	history	edited	Robert Bryant	CC BY-SA 3.0	added some missing words
May 11, 2014 at 10:10	history	edited	Robert Bryant	CC BY-SA 3.0	Fixed a grammar error in the first sentence.
May 11, 2014 at 10:08	comment	added	Robert Bryant		Of course examples exist: Just take the above construction with $\lambda=1$ and any Riemannian connection on $E$. However, as the example I gave shows, you won't always have the existence of such a connection, just sometimes.
May 11, 2014 at 9:33	comment	added	Ramand		Thank you Robert Bryant,I'm not smooth in English,and it causes problem in my question. I want an example of bundle of Lie algebras with an Invariant metric in it, admitting Riemannian connection with that property.
May 11, 2014 at 9:23	history	answered	Robert Bryant	CC BY-SA 3.0