Compact homogeneous manifolds with integrable invariant distributions, and scalar curvature

Abstract

We have studied the excitation of an atomic hydrogen by H + , Li 3+ and C 6+ ions in the range of intermediate and high impact velocities, v = 1-7 au. The theoretical method is based on a one-centre close-coupling expansion of the time-dependent wavefunction, which includes a discretized representation of the ionization continuum. The calculated cross sections are in very good agreement with the available experimental measurements up to n = 6. In contrast, some discrepancies are observed for dipole-forbidden transitions when comparing with previous theoretical data. The results show the validity of the Janev-Presnyakov scaling law for both optically-allowed and forbidden excitation transitions.

Homogeneous Riemannian manifolds of positive Ricci curvature

“…Here the fibers pass through the point H 6 M and they are equipped with the induced metric, cf. [4]. Then A and g are simply connected (because M is simply connected) and A is isometric to the Euclidean plane.…”

Solution of a Busemann problem

“…All isotropy irreducible homogeneous spaces G/H belong to the class of homogeneous spaces with integrable invariant distributions which was introduced in the author's article [28]. The articles [29,30] contain more incomplete but sufficiently advanced results about their structure and classification. Szabo's proof [17] gives a positive answer to Wolf's question in [4]: Is it possible to prove that the two-point homogeneous Riemannian spaces are symmetric without using the classification theorems?…”

Invariant intrinsic Finsler metrics on homogeneous spaces and strong subalgebras of Lie algebras

“…In [5], Berestovskiȋ obtained some results that immediately imply the following general Theorem 3 [5]. A subalgebra l in a semisimple compact Lie algebra g is strong if and only if there are decompositions into direct sums…”

“…The author is grateful to the referee for a number of useful comments, in particular, for pointing the work [5] where Theorem 3 (missing in the draft of this paper) is proved up to terminology, which allowed the author to expand the results of the present article significantly. § 1.…”