Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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RIEMANN SOLITONS ON (κ, µ)-ALMOST COSYMPLECTIC MANIFOLDS

  • Prakasha D. Gowda (Department of Studies in Mathematics Davangere University) ;
  • Devaraja M. Naik (Centre for Mathematical Needs Department of Mathematics CHRIST (Deemed to be University)) ;
  • Amruthalakshmi M. Ravindranatha (Department of Studies in Mathematics Davangere University) ;
  • Venkatesha Venkatesha (Department of Mathematics Kuvempu University)
  • Received : 2022.08.17
  • Accepted : 2022.12.22
  • Published : 2023.07.31
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Abstract

In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on (κ, µ)-almost cosymplectic manifold M with κ < 0 and we show that the soliton is expanding with ${\lambda}{\frac{\kappa}{2n-1}}(4n - 1)$ and M is locally isometric to the Lie group Gρ. Finally, we prove the non-existence of gradient almost Riemann soliton on a (κ, µ)-almost cosymplectic manifold of dimension greater than 3 with κ < 0.

Keywords

Acknowledgement

The author Amruthalakshmi M. R., is thankful to Department of Science and Technology, Ministry of Science and Technology, Government of India, for providing financial assistance through DST INSPIRE Fellowship (No: DST/INSPIRE Fellowship/[IF 190869]).

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