Browse > Article
http://dx.doi.org/10.5666/KMJ.2022.62.4.715

h-almost Ricci Solitons on Generalized Sasakian-space-forms  

Doddabhadrappla Gowda, Prakasha (Department of Mathematics, Davangere University, Shivagangothri Campus)
Amruthalakshmi Malleshrao, Ravindranatha (Department of Mathematics, Davangere University, Shivagangothri Campus)
Sudhakar Kumar, Chaubey (Section of Mathematics, Department of Information Technology, University of Technology and Applied Sciences)
Pundikala, Veeresha (Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University))
Young Jin, Suh (Department of Mathematics and RIRCM, Kyungpook National University)
Publication Information
Kyungpook Mathematical Journal / v.62, no.4, 2022 , pp. 715-728 More about this Journal
Abstract
The aim of this article is to study the h-almost Ricci solitons and h-almost gradient Ricci solitons on generalized Sasakian-space-forms. First, we consider h-almost Ricci soliton with the potential vector field V as a contact vector field on generalized Sasakian-space-form of dimension greater than three. Next, we study h-almost gradient Ricci solitons on a three-dimensional quasi-Sasakian generalized Sasakian-space-form. In both the cases, several interesting results are obtained.
Keywords
Generalized Sasakian-space-form; h-almost Ricci soliton; h-almost gradient Ricci soliton; Three-dimensional quasi-Sasakian manifold; Scalar curvature;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math., 141(2004), 157-183.    DOI
2 P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differential Geom. Appl., 26(6)(2008), 656-666.    DOI
3 P. Alegre and A. Carriazo, Submanifolds generalized Sasakian-space-forms, Taiwanese J. Math., 13(3)(2009), 923-941.    DOI
4 P. Alegre and A. Carriazo, Generalized Sasakian-space-forms and conformal change of metric, Results Math., 59(2011), 485-493.    DOI
5 A. Barros and Jr. Ribeiro, Some characterizations for compact almost Ricci solitons, Proc. Amer. Math. Soc., 140(3)(2012), 1033-1040.    DOI
6 A. L. Besse, Einstein manifolds, Classics in mathematics, Springer-Verlag, berlin(1987). 
7 D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math., Springer-Verlag(1976). 
8 C. Calin and M. Crasmareanu, From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bull. Malays. Math. Soc., 33(3)(2010), 361-368. 
9 S. K. Chaubey, U. C. De and Y. J. Suh, Kenmotsu manifolds satisfying the Fischer-Marsden equation, J. Korean Math. Soc. 58(3) (2021), 597-607.    DOI
10 S. K. Chaubey and Y. J. Suh, Ricci-Bourguignon solitons and Fischer-Marsden conjecture on generalized Sasakian-space-forms with β-Kenmotsu structure, J. Korean Math. Soc. (2023), https://doi.org/10.4134/JKMS.j220057.    DOI
11 S. K. Chaubey and G.-E. Vlcu, Gradient Ricci solitons and Fischer-Marsden equation on cosymplectic manifolds, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM 116(4) (2022), Paper No. 186, 14 pp. 
12 J. T. Cho, Ricci solitons in almost contact geometry, Proceedings of the 17th International Workshop on Differential Geometry [Vol. 17], 8595, Natl. Inst. Math. Sci. (NIMS), Taejon(2013). 
13 J. T. Cho and R. Sharma, Contact geometry and Ricci solitons, Int. J. Geom. Methods Mod. Phys., 7(6)(2010), 951-960.    DOI
14 U. C. De and A. Sarkar, On the projective curvature tensor of generalized Sasakian-space-forms, Quaest. Math., 33(2)(2010), 245-252.    DOI
15 K. Erken, Yamabe solitons on three-dimensional normal almost paracontact metric manifolds, Period. Math. Hungar., 80(2)(2020), 172-184.    DOI
16 A. Ghosh, Certain contact metrics as Ricci almost solitons, Results Math., 65 (1-2)(2014), 81-94.    DOI
17 A. Ghosh and R. Sharma, Sasakian metric as a Ricci soliton and related results, J. Geom. Phys., 75(2013), 1-6.    DOI
18 A. Ghosh and R. Sharma, K-contact metrics as Ricci solitons, Beitr. Algebra Geom., 53(1)(2012), 25-30.    DOI
19 A. Ghosh and D. S. Patra, The k-almost Ricci solitons and contact geometry, J. Korean Math. Soc., 55(1)(2018), 161-174.    DOI
20 R. Hamilton, The formation of singularities in the Ricci flow, Surveys in differential geometry, Int. Press, Cambridge(1995). 
21 R. Hamilton, The Ricci flow on surfaces, Contemp. Math., 71(1988), 237-262.    DOI
22 S. K. Hui and A. Sarkar, On the W2-curvature tensor of generalized Sasakian-space-forms, Math. Pannon., 23(1)(2012), 113-124. 
23 S. K. Hui and D. G. Prakasha, On the C-Bochner curvature tensor of generalized Sasakian-space-forms, Proc. Nat. Acad. Sci. India Sect. A, 85(3)(2015), 401-405.    DOI
24 S. K. Hui, D. G. Prakasha and V. Chavan, On generalized φ-recurrent generalized Sasakian-space-forms, Thai J. Math., 15(2)(2017), 323-332. 
25 S. K. Hui, S. Uddin, A. H. Alkhaldi and P. Mandal, Invariant submanifolds of generalized Sasakian-space-forms, Int. J. Geom. Methods Mod. Phys., 15(9)(2018), 21pp. 
26 D. Kar and P. Majhi, β-almost Ricci solitons on almost co-Kahler manifolds, Korean J. Math., 27(3)(2019), 691-705.    DOI
27 U. K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note Mat., 26(1)(2006), 55-67. 
28 P. Majhi and U. C. De, On three dimensional generalized Sasakian-space-forms, J. Geom., 108(3)(2017), 1039-1053.    DOI
29 P. Majhi and D. Kar, β-almost Ricci solitons on Sasakian 3-manifolds, Cubo, 21(3)(2019), 63-74.    DOI
30 Z. Olszak, Normal almost contact metric manifolds of dimension three, Ann. Polon. Math., 47(1986), 41-50.    DOI
31 S. Pahan, T Dutta and A. Bhattacharyya, Ricci solitons and η-Ricci solitons on generalized Sasakian-space-forms, Filomat, 31(13)(2017), 4051-4062.    DOI
32 D. G. Prakasha and H. G. Nagaraja, On quasi-conformally flat and quasi-conformally semisymmetric generalized Sasakian-space-forms, Cubo, 15(3)(2013), 59-70.    DOI
33 G. Perelman, Ricci flow with surgery on three-manifolds, preprint, arXiv:math.DG/0303109. 
34 S. Pigola, M. Rigoli, M. Rimoldi and A. Setti, Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci., 10(4)(2011), 757-799. 
35 D. G. Prakasha, On generalized Sasakian-space-forms with Weyl-conformal curvature tensor, Lobachevskii J. Math., 33(3)(2012), 223-228.    DOI
36 D. G. Prakasha and V. Chavan, E-Bochner curvature tensor on generalized Sasakian-space-forms, C. R. Math. Acad. Sci. Paris, 354(8)(2016), 835-841.    DOI
37 A. Sarkar, M. Sen and A. Akbar, Generalized Sasakian-space-forms with conharmonic curvature tensor, Palest. J. Math., 4(1)(2015), 84-90. 
38 R. Sharma, Almost Ricci solitons and K-contact geometry, Monatsh. Math., 175(2014), 621-628.    DOI
39 Q. Wang, J. N. Gomes and C. Xia, On the h-almost Ricci soliton, J. Geom. Phys., 114(2017), 216-222.    DOI
40 Y. Wang, U. C. De and X. Liu, Gradient Ricci solitons on almost Kenmotsu manifolds, Publ. Inst. Math., 98(2015), 227-235.    DOI
41 Y. Wang, Cotton tensors on almost coKahler 3-manifolds, Ann. Polon. Math., 120(2)(2017), 135-148.   DOI