<s>
In	O
mathematics	O
,	O
a	O
Hadamard	B-Algorithm
manifold	I-Algorithm
,	O
named	O
after	O
Jacques	O
Hadamard	O
—	O
more	O
often	O
called	O
a	O
Cartan	O
–	O
Hadamard	B-Algorithm
manifold	I-Algorithm
,	O
after	O
Élie	O
Cartan	O
—	O
is	O
a	O
Riemannian	B-Architecture
manifold	I-Architecture
that	O
is	O
complete	O
and	O
simply	O
connected	O
and	O
has	O
everywhere	O
non-positive	O
sectional	O
curvature	O
.	O
</s>
<s>
By	O
Cartan	O
–	O
Hadamard	O
theorem	O
all	O
Cartan	O
–	O
Hadamard	B-Algorithm
manifolds	I-Algorithm
are	O
diffeomorphic	O
to	O
the	O
Euclidean	O
space	O
Furthermore	O
it	O
follows	O
from	O
the	O
Hopf	O
–	O
Rinow	O
theorem	O
that	O
every	O
pairs	O
of	O
points	O
in	O
a	O
Cartan	O
–	O
Hadamard	B-Algorithm
manifold	I-Algorithm
may	O
be	O
connected	O
by	O
a	O
unique	O
geodesic	O
segment	O
.	O
</s>
