Generalized H-almost Ricci Soliton in Almost Kenmotsu Manifold

Authors

  • Robert Sumlalsanga Mizoram University, India
  • J. P. Singh Central University of South Bihar, India
  • M. Sundararajan Mizoram University, India

DOI:

https://doi.org/10.22232/stj.2024.12.02.08

Keywords:

b-almost, Ricci soliton, Almost Kenmotsu manifold, Hyperbolic space, Warped product

Abstract

The primary objective of this paper is to give geometric classifications for h-almost Ricci soliton associated with almost Kenmotsu manifolds. Initially, we demonstrate that a complete Kenmotsu manifold with a generalized h-almost Ricci structure is either 7-Einstein or its soliton is steady under specific circumstances. Subsequently, it is proved that a Kenmotsu manifold (k, ç)', with h' 0, it shows expansion with a generalized b-almost Ricci metric. 

Author Biographies

Robert Sumlalsanga, Mizoram University, India

Department of Mathematics and Computer Science

J. P. Singh, Central University of South Bihar, India

Department of Mathematics

M. Sundararajan, Mizoram University, India

Department of Mathematics and Computer Science

References

Bejan C. L. and Crasmareanu M. (2011). “Ricci solitons in manifolds with quasi-constant curvature", Publ. Math. Debrecen 78(1), 235-243.

Blair D. E. (2010). "Riemannian geometry of contact and symplectic manifolds", 2nd edition, Progress in Mathematics, 203, Birkh auser Boston, Ltd., Boston, MA.

Cao H.-D. (2010). "Recent progress on Ricci solitons, in Recent advances in geometric analysis", 1-38, Adv. Lect. Math. (ALM), 11, Int. Press, Somerville, MA, 2010.

Chow B., Lu P., Ni L. (2006). "Hamilton's Ricci flow", Graduate Studies in Mathematics 77.

Dileo G. and Pastore A. M. (2007). "Almost Kenmotsu manifolds and local symmetry", Bull. Belg. Math. Soc. Simon Stevin 14(2), 343-354.

Dileo G. and Pastore A. M. (2009). "Almost Kenmotsu manifolds and nullity distributions", J. Geom. 93(1-2), 46–61.

Ghosh, A. (2019). "Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold", Carpathian Math. Publ. 11(1), 56-69.

Ghosh, A. (2008). "Contact metric manifolds with η- parallel torsion tensor", Ann. Glob. Anal. Geom. 34, 287-299.

Gomes J. N., Wang Q., Xia C. (2017). "On the H-almost Ricci soliton". J. of Geom. and Phy. 114, 216–222.

Hamilton R. S. (1982). “Three-manifolds with positive Ricci curvature", J. Diff. Geom. 17(2), 255-306.

"

Kenmotsu K. (1972). A class of almost contact Riemannian manifolds", Tohoku Math. J. 24(2), 93–103.

Khatri M. and Singh J. P. (2023). "Generalized m-quasi-Einstein structure in almost Kenmotsu manifolds", Bull. Korean Math. Soc. 60, 717-732.

Sinha B. B. and Sharma R. (2011). “On Para-A-Einstein manifolds", Publications De L'Institut Mathematique, Nouvelle serie, tome 34(48), 211-215.

Shi W.-X. (1989). "Deforming the metric on complete Riemannian manifolds", J. Diff. Geom. 30(1), 223–301.

Tripathi M. M. (2008). “Ricci solitons in contact metric manifolds". arXiv:0801, 4222v1, [math DG].

Vanhecke L. and Janssens D. (1981). "Almost contact structures and curvature tensors", Kodai Math. J. 4(1), 1-27.

Wang Y. and Liu X. (2016). "On almost Kenmotsu manifolds satisfying some nullity distributions", Proc. Nat. Acad. Sci. India Sect. A, 86(3), 347-353.

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Published

2025-10-07

How to Cite

Robert Sumlalsanga, J. P. Singh, & M. Sundararajan. (2025). Generalized H-almost Ricci Soliton in Almost Kenmotsu Manifold. Science & Technology Journal, 12(2). https://doi.org/10.22232/stj.2024.12.02.08