Critical point equation on $K$-contact generalized Sasakian space form

Authors

  • R. C. Pavithra Department of Mathematics, Bangalore University, Jnanabharathi, Bengalure, Karnataka, India
  • H. G. Nagaraja Department of Mathematics, Bangalore University, Jnanabharathi, Bengalure, Karnataka, India

DOI:

https://doi.org/10.3842/umzh.v78i3-4.9409

Keywords:

$K$-contact generalized Sasakian space form,, Miao-Tam equation,, Euler-Lagranges equation,, Fischer-Marsden equation,, Einstein manifold.

Abstract

UDC 514.7

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 $S^{2n+1}$. 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.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 3-4, 2026.

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Published

28.03.2026

Issue

Vol. 78 No. 3-4 (2026)

Section

Research articles