6,059 research outputs found
Finite W_3 Transformations in a Multi-time Approach
Classical {\W} transformations are discussed as restricted diffeomorphism
transformations (\W-Diff) in two-dimensional space. We formulate them by using
Riemannian geometry as a basic ingredient. The extended {\W} generators are
given as particular combinations of Christoffel symbols. The defining equations
of \W-Diff are shown to depend on these generators explicitly. We also consider
the issues of finite transformations, global transformations and
\W-Schwarzians.Comment: 10 pages, UB-ECM-PF 94/20, TOHO-FP-9448, QMW-PH-94-2
Riemann-Christoffel flows
A geometric flow based in the Riemann-Christoffel curvature tensor that in
two dimensions has some common features with the usual Ricci flow is presented.
For dimensional spaces this new flow takes into account all the components
of the intrinsic curvature. For four dimensional Lorentzian manifolds it is
found that the solutions of the Einstein equations associated to a "detonant"
sphere of matter, as well, as a Friedman-Roberson-Walker cosmological model are
examples of Riemann-Christoffel flows. Possible generalizations are mentioned.Comment: 3 pages, RevTex,small changes, Int. J. Theor. Phys. (in press
The curvature of semidirect product groups associated with two-component Hunter-Saxton systems
In this paper, we study two-component versions of the periodic Hunter-Saxton
equation and its -variant. Considering both equations as a geodesic flow
on the semidirect product of the circle diffeomorphism group \Diff(\S) with a
space of scalar functions on we show that both equations are locally
well-posed. The main result of the paper is that the sectional curvature
associated with the 2HS is constant and positive and that 2HS allows for a
large subspace of positive sectional curvature. The issues of this paper are
related to some of the results for 2CH and 2DP presented in [J. Escher, M.
Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page
- …