A unitary manifold is a closed even-dimensional smooth manifold whose tangent bundle becomes a complex vector bundle after addition of a trivial real vector bundle of suitable even rank. The choice of this stable complex structure is part of the data. It is weaker than an almost complex structure, which acts on the tangent bundle itself. Circle group actions preserving the stable complex structure are considered in the Kosniowski conjecture (Lü et al. 2026).
Unitary Manifold
See also
Almost Complex Structure, Complex Cobordism, Kosniowski Conjecture, Tangent BundleExplore with Wolfram|Alpha
References
Lü, Z.; Ma, J.; and Tan, Q. "Unitary
-Manifolds with Four Fixed Points and Kosniowski's Conjecture."
16 Oct 2026. https://arxiv.org/abs/2610.23855.
Cite this as:
Weisstein, Eric W. "Unitary Manifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnitaryManifold.html