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<p>We investigate the critical-point equation within the framework of <i>K</i>-contact generalized Sasakian space forms. It is demonstrated that a complete <i>K</i>-contact generalized Sasakian space form satisfying the Miao–Tam equation is necessarily Einstein and isometric to the unit sphere <i>S</i><sup>2<i>n</i>+1</sup><i>.</i> In addition, we show that if this space form satisfies the Euler–Lagrange equation corresponding to the total scalar curvature functional, then it is Einstein and also satisfies the Fischer–Marsden equation. An illustrative example is provided to support and validate our theoretical findings.</p>

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Critical Point Equation on K-Contact Generalized Sasakian Space Form

  • 期刊论文

  • 发表日期：

    2026年5月23日

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  • R. C. Pavithra,
  • H. G. Nagaraja

摘要

We investigate the critical-point equation within the framework of K-contact generalized Sasakian space forms. It is demonstrated that a complete K-contact generalized Sasakian space form satisfying the Miao–Tam equation is necessarily Einstein and isometric to the unit sphere S2n+1. In addition, we show that if this space form satisfies the Euler–Lagrange equation corresponding to the total scalar curvature functional, then it is Einstein and also satisfies the Fischer–Marsden equation. An illustrative example is provided to support and validate our theoretical findings.