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A basic inequality for submanifolds in a cosymplectic space form

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  • Jeong-Sik Kim
  • Jaedong Choi

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.

Suggested Citation

  • Jeong-Sik Kim & Jaedong Choi, 2003. "A basic inequality for submanifolds in a cosymplectic space form," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:573089
    DOI: 10.1155/S0161171203202027
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    Cited by:

    1. Bang-Yen Chen & Gabriel-Eduard Vîlcu, 2023. "Recent Developments on the First Chen Inequality in Differential Geometry," Mathematics, MDPI, vol. 11(19), pages 1-50, October.

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