On basic curvature identities for almost (para)contact metric manifolds

2012/09/21 by Joanna Wełyczko, Wełyczko, Joanna
Mathematics · Physics and Astronomy · #53C15 #53C50 #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.1209.4731

openalex publication_date 2012/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In monograph of D. E. Blair "Riemannian geometry of contact and symplectic manifolds" and in the paper of S. Zamkovoy "Canonical connections on paracontact manifolds", the curvature identities respectively for contact and paracontact metric manifold are proved. We obtain the curvature identity in the wider class of manifolds, which generalizes results presented in above mentioned publications. Moreover, we present some properties of almost (para)hermitian structure on a special semiproduct of R+ and an almost (para)contact metric manifold. This semiproduct plays an auxiliary role in proving main theorem.

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