Displaying similar documents to “Free fall motion in an invariant field of forces: the 2D-case.”

On the geometry of some para-hypercomplex Lie groups

H. R. Salimi Moghaddam (2009)

Archivum Mathematicum

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In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been...

Spectral isolation of bi-invariant metrics on compact Lie groups

Carolyn S. Gordon, Dorothee Schueth, Craig J. Sutton (2010)

Annales de l’institut Fourier

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We show that a bi-invariant metric on a compact connected Lie group G is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric g 0 on G there is a positive integer N such that, within a neighborhood of g 0 in the class of left-invariant metrics of at most the same volume, g 0 is uniquely determined by the first N distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where G is simple, N can be chosen...