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Let $M$ be a $2 m$ -dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on $m$ -forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a hemisphere that have the same Hodge spectrum on 1- forms, and hyperbolic surfaces, mutually isospectral on 1-forms, with different injectivity radii. The Hodge $m$ -spectrum also does not distinguish orbifolds from manifolds....

Branson's $Q$ -curvature in Riemannian and spin geometry.

Hijazi, Oussama, Raulot, Simon (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

$C^{*}$ -algebras, positive scalar curvature, and the Novikov conjecture

Jonathan Rosenberg (1983)

Publications Mathématiques de l'IHÉS

Calcul du spectre de certaines nilvariétés compactes de dimension 3

Yves Colin de Verdière (1983/1984)

Séminaire de théorie spectrale et géométrie

Calibrated geometries in Grassmann manifolds.

W. Ziller, H. Gluck, F. Morgan (1989)

Commentarii mathematici Helvetici

Canonical forms for separability structures with less than five Killing tensors

Sergio Benenti, Mauro Francaviglia (1981)

Annales de l'I.H.P. Physique théorique

Canonical metric on the domain of discontinuity of a kleinian group

Hiroyasu Izeki, Shin Nayatani (1997/1998)

Séminaire de théorie spectrale et géométrie

Certain connections between time functions and compact spacelike submanifolds

Andrzej Derdziński (1978)

Colloquium Mathematicae

Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds.

Stefan Peters (1984)

Journal für die reine und angewandte Mathematik

Cheeger's inequality with a boundary term.

M.N. Huxley (1983)

Commentarii mathematici Helvetici

Clodes Geodesics on Non-Compact Riemannian Manifolds.

Gudlaugur Thorbergsson (1978)

Mathematische Zeitschrift

Closed Geodesics on Complete Surfaces.

Victor Bangert (1980)

Mathematische Annalen

Closed geodesics on surfaces of genus 0

Wilhelm Klingenberg (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Cohomogeneity and positive curvature in low dimensions.

Catherine Searle (1993)

Mathematische Zeitschrift

Collapse of warped submersions

Szymon M. Walczak (2006)

Annales Polonici Mathematici

We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds $(M, g_{M})$ and $(B, g_{B})$ in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric $g_{f}$ on M by $g_{f} |_{\times} \equiv g_{M} |_{\times}, g_{f} {|_{\times T M ̂} \equiv f ̂ ² g_{M} |}_{\times T M ̂}$ , where and denote the bundles of horizontal and vertical vectors. The manifold $(M, g_{f})$ obtained that way is called a warped submersion. The function f is called a warping function. We show a necessary...

Collapsing and soul theorem in three-dimension

Tatao Yamaguchi (1996/1997)

Séminaire de théorie spectrale et géométrie

Collapsing of Riemannian manifolds and eigenvalues of La-place operator.

K. Fukaya (1987)

Inventiones mathematicae

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