5 papers
-curvatures in higher dimensions and the Hirachi conjecture
Jeffrey S. Case, Yuya Takeuchi
We construct higher-dimensional analogues of the -curvature of Case and Gover in all CR dimensions . Our -curvatures all transform b…
Nonnegativity of the CR Paneitz operator for embeddable CR manifolds
Yuya Takeuchi
The nonnegativity of the CR Paneitz operator plays a crucial role in three-dimensional CR geometry. In this paper, we prove this nonnegativity for embeddable CR manifolds. This res…
Stability of the existence of a pseudo-Einstein contact form
Yuya Takeuchi
A pseudo-Einstein contact form plays a crucial role in defining some global invariants of closed strictly pseudoconvex CR manifolds. In this paper, we prove that the existence of a…
A Constraint on Chern Classes of Strictly Pseudoconvex CR Manifolds
Yuya Takeuchi
This short paper gives a constraint on Chern classes of closed strictly pseudoconvex CR manifolds (or equivalently, closed holomorphically fillable contact manifolds) of dimension…
On the second variation of the Graham-Witten energy
Yuya Takeuchi
The area renormalization procedure gives an invariant of even-dimensional closed submanifolds in a conformal manifold, which we call the Graham-Witten energy, and it is a generaliz…