Positively Curved Riemannian Locally Symmetric Spaces are Positively Squared Distance Curved
2013 ◽
Vol 65
(4)
◽
pp. 757-767
◽
Keyword(s):
Rank One
◽
AbstractThe squared distance curvature is a kind of two-point curvature the sign of which turned out to be crucial for the smoothness of optimal transportation maps on Riemannian manifolds. Positivity properties of that new curvature have been established recently for all the simply connected compact rank one symmetric spaces, except the Cayley plane. Direct proofs were given for the sphere, and an indirect one (via the Hopf fibrations) for the complex and quaternionic projective spaces. Here, we present a direct proof of a property implying all the preceding ones, valid on every positively curved Riemannian locally symmetric space.
1995 ◽
Vol 15
(5)
◽
pp. 813-820
◽
2021 ◽
Vol 494
(1)
◽
pp. 124561
2015 ◽
Vol 25
(3)
◽
pp. 815-859
◽
2012 ◽
Vol 12
(2)
◽
pp. 1165-1181
◽
1989 ◽
Vol 111
(1-2)
◽
pp. 61-67