Eigenvalues of the Laplacian of Riemannian manifolds

DOI10.2748/tmj/1178241341zbMath0266.53033OpenAlexW2119696697WikidataQ115227175 ScholiaQ115227175MaRDI QIDQ2562522

Shukichi Tanno

Publication date: 1973

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178241341

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (31)

Geometric structures and the Laplace spectrum, Part II ⋮ Spectral isolation of naturally reductive metrics on simple Lie groups ⋮ Spectral isolation of bi-invariant metrics on compact Lie groups ⋮ The G-invariant spectrum and non-orbifold singularities ⋮ A characterization of the canonical spheres by the spectrum ⋮ The spectrum of Sasakian manifolds ⋮ Spectral geometry of closed minimal submanifolds in a space form, real or complex ⋮ Unnamed Item ⋮ Spectral determination of semi-regular polygons ⋮ First nonzero eigenvalue of a minimal hypersurface in the unit sphere ⋮ Toric aspects of the first eigenvalue ⋮ The spectrum of the Laplace operator for a special Riemannian manifold ⋮ Equivariant inverse spectral theory and toric orbifolds ⋮ First nonzero eigenvalue of a pseudo-umbilical hypersurface in the unit sphere ⋮ A characterization of a complex projective space by the spectrum ⋮ Hearing the weights of weighted projective planes ⋮ Isospectral manifolds with different local geometries ⋮ Riemannian invariants that characterize rotational symmetries of the standard sphere ⋮ Spectral geometry for Riemannian foliations ⋮ Traceless component of the conformal curvature tensor in Kähler manifold ⋮ Isospectrality for spherical space forms ⋮ The spectral rigidity of complex projective spaces, revisited ⋮ Spectral uniqueness of bi-invariant metrics on symplectic groups ⋮ On lens spaces which are isospectral but not isometric ⋮ Hearing Delzant polytopes from the equivariant spectrum ⋮ The length spectrum of Riemannian two-step nilmanifolds1 ⋮ On spectral geometry of minimal parallel submanifolds ⋮ Heat invariants of the Steklov problem ⋮ A characterization of the product of two 3-spheres by the spectrum ⋮ Characterizations of some product manifolds by their spectrum ⋮ Curvature bounds for the spectrum of a compact Riemannian manifold of constant scalar curvature

Cites Work

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• On the holonomy groups of Kählerian manifolds with vanishing Bochner curvature tensor
• Compact conformally flat Riemannian manifolds
• Curvature and the eigenvalues of the Laplacian
• Curvature and the eigenforms of the Laplace operator
• On eigen-values of Laplacian and curvature of Riemannian manifold
• Euler-Poincaré characteristics and curvature tensors
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• On the Holonomy Group of the Conformally Flat Riemannian Manifold
• An inequality for $4$-dimensional Kählerian manifolds
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS
• Can One Hear the Shape of a Drum?

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