A basic inequality for submanifolds in a cosymplectic space form

2002/06/04 by Jeong-Sik Kim, Kim, Jeong-Sik, Jaedong Choi +1 · 1 citation
Mathematics · Physics and Astronomy · #53C40 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Point processes and geometric inequalities #math-ph #math.DG #math.MP #msc:53C40 #msc:53D15

paper · pdf · doi:10.48550/arxiv.math-ph/0206002

Latex 9 pages

arxiv created 2002/06/04 · openalex publication_date 2002/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely squared mean curvature on the other side. Some applications including inequalities between the intrinsic invariant δ_M and the squared mean curvature are given. The equality cases are also discussed

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