ar X iv : 0 80 9 . 45 71 v 1 [ m at h . D G ] 2 6 Se p 20 08 SubRiemannian geometry on the sphere S 3
نویسنده
چکیده
The study of step 2 subRiemannian manifolds has the Heisenberg group as a prototype. This is a noncommutative Lie group with the base manifold R and endowed with a nonintegrable distribution spanned by two of the noncommutative left invariant vector fields. This structure enjoys also the property of being a contact structure or a CR-manifold. The study of the subRiemannian geodesics on the Heisenberg group started with the work of Gaveau [9]. One trend in the literature is to use the geometry of the Heisenberg group to describe the Heisenberg Laplacian and its heat kernel, see Beals, Gaveau, Greiner [1,2,3,4]. Later, this structure led to generalizations of the Heisenberg group as can be seen in Calin, Chang, Greiner [5,6] and Chang, Markina [7]. For more fundamental issues on subRiemannian geometry, see Strichartz [10].
منابع مشابه
ar X iv : 0 80 9 . 47 83 v 1 [ m at h . C A ] 2 7 Se p 20 08 HEAT - FLOW MONOTONICITY OF STRICHARTZ NORMS
Most notably we prove that for d = 1, 2 the classical Strichartz norm ‖ef‖ L 2+4/d s,x (R×Rd) associated to the free Schrödinger equation is nondecreasing as the initial datum f evolves under a certain quadratic heat-flow.
متن کاملar X iv : 0 80 9 . 26 64 v 1 [ m at h . A P ] 1 6 Se p 20 08 Balance laws with integrable unbounded sources ∗
We consider the Cauchy problem for a n×n strictly hyperbolic system of balance laws
متن کاملar X iv : 0 80 9 . 40 53 v 1 [ m at h . C A ] 2 3 Se p 20 08 SOME EXTREMAL FUNCTIONS IN FOURIER ANALYSIS , III
We obtain the best approximation in L 1 (R), by entire functions of exponential type, for a class of even functions that includes e −λ|x| , where λ > 0, log |x| and |x| α , where −1 < α < 1. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.
متن کاملar X iv : 0 80 2 . 44 39 v 1 [ m at h . D G ] 2 9 Fe b 20 08 Poisson geometry and first integrals of geostrophic equations
We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry behind this similarity, give several equivalent definitions of the Poisson structure on the space of smooth densities on a symplectic manifold, and show how it can be obtained via the Hamiltonian reduction from a sym...
متن کاملar X iv : 0 80 2 . 25 80 v 1 [ m at h . G T ] 1 9 Fe b 20 08 3 - Dimensional Schlaefli Formula and Its Generalization
Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.
متن کامل