The first eigenvalue of the laplacian for a positively curved homogeneous riemannian manifold

Hajime Urakawa

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On the spectrum of Riemannian submersions with totally geodesic fibers

Gérard Besson, Manlio Bordoni (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.

Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix

Yana Alexieva, Stefan Ivanov (1999)

Archivum Mathematicum

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Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures $r_{1} = r_{2} = 0, r_{3} \neq 0$ , which are not locally homogeneous, in general.

Higher order geodesic symmetries

García, A., Jiménez, J. A., Sánchez, C. U.

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