Warped product contact CR-submanifolds of globally framed f-manifolds with Lorentz metric

2012/04/27 by Khushwant Singh, Singh, Khushwant, S. S. Bhatia +1
Mathematics · #53B25 #53C25 #53C40 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.AG #math.DG #msc:53B25 #msc:53C25 #msc:53C40

paper · pdf · doi:10.48550/arxiv.1204.6125

arXiv admin note: text overlap with arXiv:1106.6317

arxiv created 2012/04/27 · openalex publication_date 2012/04/27 · arxiv updated 2012/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if M = N^⊥ ×_f N^T is a warped CR-submanifold such that N^⊥ is ϕ?-anti-invariant and NT is ϕ?-invariant, then M is a CR-product. We show that the second fundamental form of a contact CR warped product of a indefinite S space form satisfies a geometric inequality, ‖h‖² ≥ p3‖∇ lnf‖² - \triangle lnf + (c + 2)k + 1.

Citations

• An Osserman-type condition on g.f.f-manifolds with Lorentz metric
• Riemannian Geometry of Contact and Symplectic Manifolds
• Manifolds of negative curvature

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