A remark on four-dimensional almost Kähler-Einstein manifolds with negative scalar curvature
Concerning the Goldberg conjecture, we will prove a result obtained by applying the result of Iton in terms of L2-norm of the scalar curvature.
Notes on the Goldberg Conjecture in Dimension Four
Concerning the integrability of almost Kahler manifolds, there is a longstanding conjecture by S.I. Goldberg, “A compact almost Kahler Einstein manifold is Kahler”. The conjecture is true in the case where the scalar curvature is non-negative. However, the conjecture is still open in the remaining case. In this note, we shall give a brief survey on the recent progress concerning the conjecture in four-dimensional case.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.