Explicit formulas for the Hodge-Laplacian spectrum on 1-forms of homogeneous 3-spheres are derived, and this spectrum determines the metric up to isometry.
Milnor,Curvatures of left-invariant metrics on Lie groups
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
fields
math.DG 3verdicts
UNVERDICTED 3representative citing papers
Equivalent conditions on the structure equations of 3D Lie algebras determine which left-invariant pseudo-Riemannian metrics admit left-invariant harmonic spinors.
Moduli spaces of left-invariant statistical structures are introduced and computed on three Lie groups with unique left-invariant metrics, yielding classifications of conjugate-symmetric and dually-flat structures.
citing papers explorer
-
Hodge Laplacian on $1$-forms of homogeneous $3$-spheres
Explicit formulas for the Hodge-Laplacian spectrum on 1-forms of homogeneous 3-spheres are derived, and this spectrum determines the metric up to isometry.
-
Left-invariant harmonic spinors on three-dimensional Lie groups
Equivalent conditions on the structure equations of 3D Lie algebras determine which left-invariant pseudo-Riemannian metrics admit left-invariant harmonic spinors.
-
The moduli spaces of left-invariant statistical structures on Lie groups
Moduli spaces of left-invariant statistical structures are introduced and computed on three Lie groups with unique left-invariant metrics, yielding classifications of conjugate-symmetric and dually-flat structures.