arXiv subjects

Shuhei Yonehara

Publications and source records attributed to Shuhei Yonehara.

4 recordsLinked to original sources

arXiv2026

Godbillon-Vey classes of Lie subalgebroids

The Godbillon-Vey class is a secondary characteristic class which is defined for regular foliations and have been studied extensively. On the other hand, extending the Godbillon-Vey class to singular foliations is difficult, and a complete result has not yet been obtained. In this paper, we address this problem by focusing on a geometric object called a Lie algebroid on a manifold. More precisely, we fix a Lie algebroid and relatively define the Godbillon-Vey class for its Lie subalgebroids, and study their properties. We also present several examples.

math.DG↗

arXiv2026

Godbillon-Vey classes of regular Jacobi manifolds

The notion of a Jacobi manifold is a natural generalization of that of a Poisson manifold. A Jacobi manifold has a natural foliation in which each leaf has either a contact structure or a locally conformal symplectic structure. In this paper, we study a characteristic class called the Godbillon-Vey class for Jacobi manifolds with regular foliation and express it explicitly in terms of Jacobi structures.

math.DG↗

arXiv2025

Mikami-Weinstein Type Theorem for Cosymplectic Groupoid Actions

The Mikami-Weinstein theorem is a generalization of the classical Marsden-Weinstein-Meyer symplectic reduction theorem to the case of symplectic groupoid actions. In this paper, we introduce the notion of a cosymplectic groupoid action on a cosymplectic manifold and prove a theorem which is a natural analogue of the Mikami-Weinstein theorem.

math.SG↗

arXiv2024

Reduction of coKähler and 3-cosymplectic manifolds

The notions of coKähler manifolds and 3-cosymplectic manifolds are odd-dimensional analogues of the ones of Kähler manifolds and hyperKähler manifolds, respectively. In this paper, we obtain reduction theorems of coKähler manifolds and 3-cosymplectic manifolds. We show that Kähler and coKähler (hyperKähler and 3-cosymplectic) reductions admit a natural compatibility with respect to ``cylinder constructions". We further prove the compatibility of Kähler and coKähler reductions with respect to the "mapping torus construction".

math.SG↗