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Warped Product Semi-Invariant Submanifolds in Almost Paracontact Riemannian Manifolds

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  • Mehmet Atçeken

Abstract

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form ð ‘ = ð ‘ âŸ‚ × ð ‘“ ð ‘ ð ‘‡ by reversing two factor manifolds ð ‘ ð ‘‡ and ð ‘ âŸ‚ . We prove several fundamental properties of warped product semi-invariant submanifolds in an almost paracontact Riemannian manifold and establish a general inequality for an arbitrary warped product semi-invariant submanifold. After then, we investigate warped product semi-invariant submanifolds in a general almost paracontact Riemannian manifold which satisfy the equality case of the inequality.

Suggested Citation

  • Mehmet Atçeken, 2009. "Warped Product Semi-Invariant Submanifolds in Almost Paracontact Riemannian Manifolds," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-16, September.
    • Handle: RePEc:hin:jnlmpe:621625
    DOI: 10.1155/2009/621625
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