ケーラー多様体
for tangent vectors "u" and "v" (where "i" is the complex number formula_3). For a Kähler manifold "X", the Kähler form "ω" is a real closed (1,1)-form. A Kähler manifold can also be viewed as a Riemannian manifold, with the Riemannian metric "g" defined by