3 added 166 characters in body

According to Scott's paper "The geometries of 3-manifolds", the only closed manifolds that admit an $S^2\times R$ geometry are the two $S^2$ bundles over $S^1$, $P^2\times S^1$ and $P^3\sharp P^3$. It seems like the last one is the only candidate (unless I'm missing a way in which $S^2\times S^1$ can be viewed as such a bundle).

(How do I get a connect sum symbol in maths mode!?)

EDIT: Used \sharp as Richard suggested.

FURTHER EDIT: As pointed out below, I spoke too soon. Of course such bundles could have spherical geometry too. Scott's paper is a nice reference for that too!

2 Introduced sharp

According to Scott's paper "The geometries of 3-manifolds", the only closed manifolds that admit an $S^2\times R$ geometry are the two $S^2$ bundles over $S^1$, $P^2\times S^1$ and the connect sum of two copies of $P^3$. P^3\sharp P^3$. It seems like the last one is the only candidate (unless I'm missing a way in which$S^2\times S^1$can be viewed as such a bundle). (How do I get a connect sum symbol in maths mode!?) EDIT: Used \sharp as Richard suggested. 1 According to Scott's paper "The geometries of 3-manifolds", the only closed manifolds that admit an$S^2\times R$geometry are the two$S^2$bundles over$S^1$,$P^2\times S^1$and the connect sum of two copies of$P^3$. It seems like the last one is the only candidate (unless I'm missing a way in which$S^2\times S^1\$ can be viewed as such a bundle).

(How do I get a connect sum symbol in maths mode!?)