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.
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2026 2verdicts
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A unified representation-theoretic approach computes the complete Laplace-Beltrami spectra on homogeneous principal bundles and applies the results to classify scalar stability and Yamabe bifurcations on specific manifold families.
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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.