Matches in DBpedia 2016-04 for { ?s ?p "In mathematics, a Hermitian manifold is the complex analogue of a Riemannian manifold. Specifically, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space. One can also define a Hermitian manifold as a real manifold with a Riemannian metric that preserves a complex structure.A complex structure is essentially an almost complex structure with an integrability condition, and this condition yields an unitary structure (U(n) structure) on the manifold. By dropping this condition we get an almost Hermitian manifold.On any almost Hermitian manifold we can introduce a fundamental 2-form, or cosymplectic structure, that depends only on the chosen metric and almost complex structure. This form is always non-degenerate, with the suitable integrability condition (of it also being closed and thus a symplectic form) we get an almost Kähler structure. If both almost complex structure and fundamental form are integrable, we have a Kähler structure."@en }
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- Hermitian_manifold abstract "In mathematics, a Hermitian manifold is the complex analogue of a Riemannian manifold. Specifically, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space. One can also define a Hermitian manifold as a real manifold with a Riemannian metric that preserves a complex structure.A complex structure is essentially an almost complex structure with an integrability condition, and this condition yields an unitary structure (U(n) structure) on the manifold. By dropping this condition we get an almost Hermitian manifold.On any almost Hermitian manifold we can introduce a fundamental 2-form, or cosymplectic structure, that depends only on the chosen metric and almost complex structure. This form is always non-degenerate, with the suitable integrability condition (of it also being closed and thus a symplectic form) we get an almost Kähler structure. If both almost complex structure and fundamental form are integrable, we have a Kähler structure.".
- Q5741935 abstract "In mathematics, a Hermitian manifold is the complex analogue of a Riemannian manifold. Specifically, a Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space. One can also define a Hermitian manifold as a real manifold with a Riemannian metric that preserves a complex structure.A complex structure is essentially an almost complex structure with an integrability condition, and this condition yields an unitary structure (U(n) structure) on the manifold. By dropping this condition we get an almost Hermitian manifold.On any almost Hermitian manifold we can introduce a fundamental 2-form, or cosymplectic structure, that depends only on the chosen metric and almost complex structure. This form is always non-degenerate, with the suitable integrability condition (of it also being closed and thus a symplectic form) we get an almost Kähler structure. If both almost complex structure and fundamental form are integrable, we have a Kähler structure.".