The Fact About complex geometries That No One Is Suggesting
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A Kähler manifold is a complex manifold that has a Riemannian metric and symplectic composition appropriate While using the complex composition. Each complex submanifold of a Kähler manifold is Kähler, and so particularly just about every non-singular affine or projective complex variety is Kähler, soon after restricting the typical Hermitian metric on C n displaystyle mathbb C ^ n
For example, every complex manifold is canonically orientable, and a method of Liouville's theorem retains on compact complex manifolds or projective complex algebraic types.
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