Definitions

1. Again since harmonic forms are parallel, we can reduce the calculation to the tangent space of a point, which is a symplectic vector space. (Web site)

Topological Invariants

1. One subject here is the representation of topological invariants (such as cohomology) by analytic means (such as harmonic forms). (Web site)

Differential Manifold

1. Harmonic forms For a differential manifold M, we can equip it with some auxiliary Riemannian metric.

Symplectic Vector Space

1. Again since harmonic forms are parallel, we can reduce the calculation to the tangent space of a point, which is a symplectic vector space. (Web site)

Harmonic

1. A smooth manifold is said to be geometrically formal if it admits a Riemannian metric for which all products of harmonic forms are harmonic.

Harmonic Form

1. Harmonic forms If M is a compact Riemannian manifold, then each equivalence class in H k dR(M) contains exactly one harmonic form.

Harmonic Forms

1. One generalization of the study of harmonic functions is the study of harmonic forms on Riemannian manifolds, and it is related to the study of cohomology. (Web site)
2. The harmonic forms on compact Lie groups are those differential forms that are invariant under both left and right translations of the group. (Web site)
3. We also prove that a manifold admits a metric with harmonic forms whose product is not harmonic if and only if it is not a rational homology sphere. (Web site)

Categories

1. Harmonic Form
2. Compact Riemannian Manifold
3. Symplectic Vector Space
4. Differential Manifold
5. Compact Lie Groups
6. Books about "Harmonic Forms" in Amazon.com
   

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