2023/06/05 by Vladimir Rovenski, Rovenski, Vladimir · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2306.03062
openalex publication_date 2023/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study geometry of the weak almost para-f-structure and its subclasses. This allow us to produce totally geodesic foliations and also to take a fresh look at the para-f-structure introduced by A. Bucki and A. Miernowski. We demonstrate this by generalizing several known results on almost para-f-manifolds. First, we express the covariant derivative of f using a new tensor on a metric weak para-f-structure, then we prove that on a weak para-\cal K-manifold the characteristic vector fields are Killing and ker f defines a totally geodesic foliation. Next, we show that a para-\cal S-structure is rigid (i.e., a weak para-\cal S-structure is a para-\cal S-structure), and that a metric weak para-f-structure with parallel tensor f reduces to a weak para-\cal C-structure. We obtain corollaries for p=1, i.e., for a weak almost paracontact structure.