The gap phenomenon in the dimension study of finite type systems

Boris Kruglikov

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Automorphism groups of parabolic geometries

Čap, Andreas

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Elisha Falbel, Claudio Gorodski (1995)

Annales scientifiques de l'École Normale Supérieure

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Two supergeometries from fourfold gradings of superalgebras

Lukierski, Jerzy

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Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric

Claudio Altafini (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian...

Isospectral deformations of closed riemannian manifolds with different scalar curvature

Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb, Edward N. Wilson (1998)

Annales de l'institut Fourier

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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.