Weak Almost Contact Structures: a Survey

2024/08/25 by Vladimir Rovenski, Rovenski, Vladimir · 2 citations
Engineering · #Differential Geometry (math.DG) #FOS: Mathematics #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2408.13827

openalex publication_date 2024/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Weak almost contact manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak, allowed us to take a new look at the theory of contact manifolds. The paper surveys recent results (concerning geodesic and Killing fields, rigidity and splitting theorems, Ricci-type solitons and Einstein-type metrics, etc.) in this new field of Riemannian geometry.

Cited by

• Applications of Weak Metric Structures to Non-Symmetrical Gravitational Theory
• Weak metric structures on generalized Riemannian manifolds

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