2025/04/23 by Ilka Agricola, Dario Di Pinto, Agricola, Ilka +5 · 1 citation
Mathematics · #53C10 #53C15 #53C25 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics #Fixed Point Theorems Analysis #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2504.16900
openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
In 1990, D. Chinea and C. Gonzalez gave a classification of almost contact metric manifolds into 212 classes, based on the behaviour of the covariant derivative ∇gΦ of the fundamental 2-form Φ. This large number makes it difficult to deal with this class of manifolds. We propose a new approach to almost contact metric manifolds by introducing two intrinsic endomorphisms S and h, which bear their name from the fact that they are, basically, the entities appearing in the intrinsic torsion. We present a new classification scheme for them by providing a simple flowchart based on algebraic conditions involving S and h, which then naturally leads to a regrouping of the Chinea-Gonzalez classes, and, in each step, to a further refinement, eventually ending in the single classes. This method allows a more natural exposition and derivation of both known and new results, like a new characterization of almost contact metric manifolds admitting a characteristic connection in terms of intrinsic endomorphisms. We also describe in detail the remarkable (and still very large) subclass of H-parallel almost contact manifolds, defined by the condition (∇gXΦ)(Y,Z)=0 for all horizontal vector fields, X,Y,Z\inH.