6 papers
Joint spectrum of the sub-Laplacian and the Reeb vector field on three-dimensional Heisenberg Bieberbach manifolds
Yoshiaki Suzuki, Yuya Takeuchi
A Heisenberg Bieberbach manifold is a compact quotient of the Heisenberg group by a discrete torsion-free subgroup of its pseudo-Hermitian automorphism group. In this paper, we stu…
Non-embeddable torus and CR Paneitz operator
Pak Tung Ho, Yuya Takeuchi
The CR Paneitz operator is closely related to several important problems in CR geometry. In this paper, we study the CR Paneitz operator on non-embeddable three-dimensional tori. U…
Non-homothetic complete periodic contact forms with constant Tanaka--Webster scalar curvature
Jeffrey S. Case, Yuya Takeuchi
We study the existence problem for complete contact forms with constant Tanaka--Webster scalar curvature on non-compact strictly pseudoconvex CR manifolds. We prove that, under mil…
CR Paneitz operator and embeddability
Yuya Takeuchi
In this article, we give a brief survey of recent developments on relations between global embeddability of a closed strictly pseudoconvex CR manifold and the CR Paneitz operator.
CR Paneitz operator on non-embeddable CR manifolds
Yuya Takeuchi
The CR Paneitz operator is closely related to some important problems in CR geometry. In this paper, we consider this operator on a non-embeddable CR manifold. This operator is ess…
Formulae of some global CR invariants for Sasakian -Einstein manifolds
Yuya Takeuchi
In this paper, we give explicit formulae of the Burns-Epstein invariant and global CR invariants via renormalized characteristic forms introduced by Marugame for Sasakian -Eins…