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We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on $S^{n} \times T^{m}$ , where $T^{m}$ is a torus of dimension $m \geq 2$ and $S^{n}$ is a sphere of dimension $n \geq 4$ . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds.

Dorothee Schueth (1995)

Commentarii mathematici Helvetici

Isospectral Riemann surfaces

Peter Buser (1986)

Annales de l'institut Fourier

We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus $g = 5$ and for all $g \geq 7$ . In a second part we give examples of isospectral non isometric surfaces in $R^{3}$ which are realizable by paper models.

Isotropic curvature: A survey

Harish Seshadri (2007/2008)

Séminaire de théorie spectrale et géométrie

We discuss the notion of isotropic curvature of a Riemannian manifold and relations between the sign of this curvature and the geometry and topology of the manifold.

Jacobi Fields and Finsler Metrics on Compact Lie Groups with an Application to Differentiable Pinching Problems.

Ernst A. Ruh, Karsten Grove, Hermann Karcher (1974)

Mathematische Annalen

Jacobi maps between Riemannian manifolds.

Belger, Martin, Milousheva, Velichka, Stanilov, Grozio (1995)

Beiträge zur Algebra und Geometrie

Jacobi Tensors and Ricci Curvature.

John J. O'Sullivan, Jost-Hinrich Eschenburg (1980)

Mathematische Annalen

Killing vector fields of constant length on Riemannian manifolds.

Berestovskij, V.N., Nikonorov, Yu.G. (2008)

Sibirskij Matematicheskij Zhurnal

Killing vectors and geodesic flow vectors on tangent bundles.

Shukichi Tanno (1976)

Journal für die reine und angewandte Mathematik

Konvexe Mengen in Riemannschen Mannigfaltigkeiten.

Victor Bangert (1978)

Mathematische Zeitschrift

Krümmung und differenzierbare Struktur auf Sphären, II.

Ernst A. Ruh (1973)

Mathematische Annalen

$L^{2}$ vector bundle valued forms and the Laplace-Beltrami operator

Francesco Ricci (1986)

Rendiconti del Seminario Matematico della Università di Padova

$L_{p, q}$ -cohomology of warped cylinders

Yaroslav Kopylov (2009)

Annales mathématiques Blaise Pascal

We extend some results by Gol $^{'}$ dshtein, Kuz $^{'}$ minov, and Shvedov about the $L_{p}$ -cohomology of warped cylinders to $L_{p, q}$ -cohomology for $p \neq q$ . As an application, we establish some sufficient conditions for the nontriviality of the $L_{p, q}$ -torsion of a surface of revolution.

L $_{p}$ -когомологии искривленных цилиндров.

В.М. Гольдштейн, В.И. Кузьминов, И.А. Шведов (1990)

Sibirskij matematiceskij zurnal

L2 - Curvature pinching.

Ernst A. Ruh, Maung Min-O (1990)

Commentarii mathematici Helvetici

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