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Kähler manifold - Definition | | Kähler manifold - Definition: Encyclopedia II - Kähler manifold - Definition | | A Kähler metric on a complex manifold M is a hermitian metric on the complexified tangent bundle satisfying a condition that has several equivalent characterizations (the most geometric being that parallel transport gives rise to complex-linear mappings on the tangent spaces). In terms of local coordinates it is specified in this way: if
is the hermitian metric, then the associated Kähler form (defined up to a factor of i/2) by
is closed: that is, dω = 0. If M carries such a metric it is called a Kähler manifold.
The metric on a Kähler ...
See also:Kähler manifold, Kähler manifold - Definition, Kähler manifold - Examples | | | Kähler manifold, Kähler manifold - Definition, Kähler manifold - Examples, almost complex manifold, complex manifold, Hermitian manifold, hyper-Kähler manifold, quaternion-Kähler manifold | | |
| | | Kähler manifold: Encyclopedia II - Kähler manifold - Definition
Kähler manifold - Definition
A Kähler metric on a complex manifold M is a hermitian metric on the complexified tangent bundle satisfying a condition that has several equivalent characterizations (the most geometric being that parallel transport gives rise to complex-linear mappings on the tangent spaces). In terms of local coordinates it is specified in this way: if
is the hermitian metric, then the associated Kähler form (defined up to a factor of i/2) by
is closed: that is, dω = 0. If M carries such a metric it is called a Kähler manifold.
The metric on a Kähler manifold locally satisfies
for some function K, called the Kähler potential.
Other related archivesCalabi-Yau manifolds, Complex projective space, Erich Kähler, Euclidean space, Hermitian manifold, Riemann surface, Riemannian manifolds, Riemannian metric, Stein manifold, algebraic geometry, algebraic variety, almost complex manifold, closed, compact, complex manifold, complexified, hermitian metric, hyper-Kähler manifold, lattice, manifold, mathematics, parallel transport, quaternion-Kähler manifold, symplectic form, symplectic manifolds, tangent bundle
 Adapted from the Wikipedia article "Definition", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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