Weak Nearly \mathcal S- and Weak Nearly \mathcal C- Manifolds

2025/08/25 by Rovenski, Vladimir
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17755

Abstract

The recent interest of geometers in the f-structures of K. Yano is motivated by the study of the dynamics of contact foliations, as well as their applications in theoretical physics. Weak metric f-structures on a smooth manifold, recently introduced by the author and R. Wolak, open a new perspective on the theory of classical structures. In the paper, we define structures of this kind, called weak nearly \cal S- and weak nearly \cal C- structures, study their geometry, e.g. their relations to Killing vector fields, and characterize weak nearly \cal S- and weak nearly \cal S- submanifolds in a weak nearly Kähler manifold.

Citations

• Integration on q-Cosymplectic Manifolds
• Applications of Weak Metric Structures to Non-Symmetrical Gravitational Theory
• Weak metric structures on generalized Riemannian manifolds
• Contact foliations and generalised Weinstein conjectures
• Parallel skew-symmetric tensors on 4-dimensional metric Lie algebras
• Generalized k-contact structures
• On the topology of metric f-K-contact manifolds

Related

• On the splitting of weak nearly \cal C-manifolds
• Characterizations of weak almost \mathcal S-manifolds with curvature properties
• Geometry of weak metric f-manifolds: a survey
• On the geometry of a weakened f-structure
• Foliated structure of weak nearly Sasakian manifolds