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<p>This article focuses on characterizing warped product manifolds through the flatness and the symmetry of the concircular curvature tensor. It is proved that the factor manifolds of a concircularly-flat warped product manifold have constant sectional curvatures as well as they are concircularly-flat. It is shown that in a concircularly-symmetric warped product manifold, the fiber manifold has constant sectional curvature and it is concircularly-flat, while the base manifold is locally-symmetric and concircularly-symmetric. It is demonstrated that a concircularly-flat (symmetric) GRW space-time is perfect fluid and static. Finally, it is established that in a concircularly-flat (symmetric) <i>F</i>-associated standard static space-time, the base manifold has constant sectional curvature and it is concircularly-flat, while the fiber manifold is locally-symmetric and concircularly-symmetric.</p>

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Investigations of warped product manifolds through the concircular curvature tensor with relativistic applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月28日

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  • Abdallah Abdelhameed Syied,
  • Crina Daniela Neacşu,
  • Nasser Bin Turki,
  • Gabriel-Eduard Vîlcu

摘要

This article focuses on characterizing warped product manifolds through the flatness and the symmetry of the concircular curvature tensor. It is proved that the factor manifolds of a concircularly-flat warped product manifold have constant sectional curvatures as well as they are concircularly-flat. It is shown that in a concircularly-symmetric warped product manifold, the fiber manifold has constant sectional curvature and it is concircularly-flat, while the base manifold is locally-symmetric and concircularly-symmetric. It is demonstrated that a concircularly-flat (symmetric) GRW space-time is perfect fluid and static. Finally, it is established that in a concircularly-flat (symmetric) F-associated standard static space-time, the base manifold has constant sectional curvature and it is concircularly-flat, while the fiber manifold is locally-symmetric and concircularly-symmetric.