Two-dimensional Hopf manifolds are called
Hopf surfaces.
Examples
In a typical situation, is generated
by a linear contraction, usually a
diagonal matrix, with
a
complex number, . Such manifold
is called a classical Hopf manifold.
Properties
A Hopf manifold
is
diffeomorphic to .
For , it is non-
Kähler. In fact, it is not even
symplectic because the second cohomology group is zero.
Hopf, Heinz (1948), "Zur Topologie der komplexen Mannigfaltigkeiten", Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience Publishers, Inc., New York, pp. 167–185,
MR0023054