Timeline for Examples of product negatively curved Riemannian manifolds

8 events

when toggle format	what		by	license	comment
May 29 at 2:31	history	became hot network question
May 29 at 0:33	history	edited	Yasha	CC BY-SA 4.0	added 4 characters in body
May 29 at 0:16	vote	accept	Yasha
May 28 at 22:58	answer	added	Igor Belegradek		timeline score: 3
May 28 at 22:18	comment	added	Yasha		Cool! Do you have a reference or would you like to expand it as an answer please?
May 28 at 21:08	comment	added	Igor Belegradek		Actually I take it back. There are examples where say $Y$ is a torus and $X$ is the product of a torus and a Euclidean space. Then $X\times Y$ has a complete metric of constant negative curvature. What one does not have is examples where $Y$ is closed negatively curved.
May 28 at 19:08	comment	added	Igor Belegradek		The condition "negative sectional curvature" is difficult to work with for open manifolds. Pinched negative curvature is a much easier condition, e.g. in a discrete isometry group of a negatively pinched Hadamard manifold the centralizer of any infinite order element is virtually nilpotent, so your $X\times Y$ cannot be negatively pinched. The best result I know is that if $X\times Y$ is negatively curved, the deck group of its universal cover fixes a point at infinity, see Corollary 11.6 in arxiv.org/pdf/1306.1256, which is a survey of open negatively curved manifolds.
May 28 at 18:31	history	asked	Yasha	CC BY-SA 4.0