On the rigidity of the Sasakian structure and characterization of cosymplectic manifolds

2022/03/09 by Vladimir Rovenski, Rovenski, Vladimir, Dhriti Sundar Patra +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2203.04597

openalex publication_date 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce new metric structures on a smooth manifold (called "weak" structures) that generalize the almost contact, Sasakian, cosymplectic, etc. metric structures (φ,ξ,η,g) and allow us to take a fresh look at the classical theory. We demonstrate this statement by generalizing several well-known results. We prove that any Sasakian structure is rigid, i.e., our weak Sasakian structure is homothetically equivalent to a Sasakian structure. We show that a weak almost contact structure with parallel tensor φ is a weak cosymplectic structure and give an example of such a structure on the product of manifolds. We find conditions for a vector field to be a weak contact infinitesimal transformation.

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