Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAlmost homogeneous manifolds with boundary
370
0
0.0
(
0
)
Authors
Benoit Kloeckner
Ask ChatGPT about the research
No Arabic abstract
Let $rho_0$ be an action of a Lie group on a manifold with boundary that is transitive on the interior. We study the set of actions that are topologically conjugate to $rho_0$, up to smooth or analytic change of coordinates. We show that in many cases, including the compactifications of negatively curved symmetric spaces, this set is infinite.
rate research
Read More
We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost Kahler manifolds. We give an explicit non-compact example of an Einstein almost cokahler manifold that is not cokahler. We prove that compact Einstein almost cokahler manifolds with non-negative $*$-scalar curvature are cokahler (indeed, transversely Calabi-Yau); more generally, we give a lower and upper bound for the $*$-scalar curvature in the case that the structure is not cokahler. We prove similar bounds for almost Kahler Einstein manifolds that are not Kahler.
We prove that a 2n-dimensional compact homogeneous nearly Kahler manifold with strictly positive sectional curvature is isometric to CP^{n}, equipped with the symmetric Fubini-Study metric or with the standard Sp(m)-homogeneous metric, n =2m-1, or to S^{6} as Riemannian manifold with constant sectional curvature. This is a positive answer for a revised version of a conjecture given by Gray.
We consider a class of compact homogeneous CR manifolds, that we call $mathfrak n$-reductive, which includes the orbits of minimal dimension of a compact Lie group $K_0$ in an algebraic homogeneous variety of its complexification $K$. For these manifolds we define canonical equivariant fibrations onto complex flag manifolds. The simplest example is the Hopf fibration $S^3tomathbb{CP}^1$. In general these fibrations are not $CR$ submersions, however they satisfy a weaker condition that we introduce here, namely they are CR-deployments.
We study manifolds with almost nonnegative curvature operator (ANCO) and provide first examples of closed simply connected ANCO mannifolds that do not admit nonnegative curvature operator.
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank, giving a classification of closed, smooth, simply-connected 4-manifolds of almost non-negative curvature under the assumption of torus symmetry.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
