Ricci solitons in a generalized weakly (Ricci) symmetric D-homothetically deformed Kenmotsu manifold

Adara Monica Blaga, Kanak Kanti Baishya, Nihar Sarkar

Abstract


The object of the present paper is to investigate the nature of Ricci solitons on D-homothetically deformed Kenmotsu manifold with generalized weakly symmetric and generalized weakly Ricci symmetric curvature restrictions.

Keywords


Kenmotsu manifold; D-homothetic deformation; generalized weakly symmetric manifold; generalized weakly Ricci symmetric manifold; Ricci solitons

Mathematics Subject Classification (2010)


53C15; 53C25

References


Alegre, Pablo, David E. Blair and Alfonso Carriazo. "Generalized Sasakian-spaceforms." Israel J. Math. 141 (2004): 157-183.

Baishya, Kanak Kanti "Note on almost generalized pseudo-Ricci symmetric manifolds." Kyungpook Math. J. 57, no. 3 (2017): 517-523.

Baishya, Kanak Kanti "On generalized semi-pseudo symmetric manifold." submitted.

Baishya, Kanak Kanti. "On generalized weakly symmetric manifolds." Bull. Transilv. Univ. Brasov Ser. III 10(59), no. 1 (2017): 31-38.

Baishya, Kanak Kanti. "Ricci solitons in Sasakian manifold." Afr. Mat. 28, no. 7-8 (2017): 1061-1066.

Baishya, Kanak Kanti and Roy Partha Chowdhury. "theta-Ricci solitons in (LCS)n-manifold." Bull. Transilv. Univ. Brasov Ser. III 9(58), no. 2 (2016): 1-12.

Baishya, Kanak Kanti and Partha Roy Chowdhury. "On almost generalized weakly symmetric LP-Sasakian manifolds." An. Univ. Vest Timis. Ser. Mat.-Inform. 55, no. 2 (2017): 51-64.

Baishya, Kanak Kanti et all. "On almost generalized weakly symmetric Kenmotsu manifolds." Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 55, no. 2 (2016): 5-15.

Blaga, Adara M. "theta-Ricci solitons on Lorentzian para-Sasakian manifolds." Filomat 30, no. 2 (2016): 489-496.

Blaga, Adara M. "Eta-Ricci solitons on para-Kenmotsu manifolds." Balkan J. Geom. Appl. 20, no. 1 (2015): 1-13.

Blaga, Adara M., Kanak Kanti Baishya and Nihar Sarkar. "Ricci solitons in a D-homothetically deformed Kenmotsu manifold of (Ricci) semi-symmetric type." submitted.

Blaga, Adara M. and Mircea Crasmareanu. "Torse-forming theta-Ricci solitons in almost paracontact theta-Einstein geometry." Filomat 31, no. 2 (2017): 499-504.

Blair, David E. Contact manifolds in Riemannian geometry. Vol. 509 of Lecture Notes in Mathematics. Berlin-New York: Springer-Verlag, 1976.

Cartan, E. "Sur une classe remarquable d’espaces de Riemann." Bull. Soc. Math. France 54 (1926): 214-264.

Chaki, M.C. "On pseudo symmetric manifolds." An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 33, no. 1 (1987): 53-58.

Dubey, R.S.D. "Generalized recurrent spaces." Indian J. Pure Appl. Math. 10, no. 12 (1979): 1508-1513.

Ghosh, Amalendu and Ramesh Sharma. "K-contact metrics as Ricci solitons." Beitr. Algebra Geom. 53, no. 1 (2012): 25-30.

Hamilton, Richard S. "The Ricci flow on surfaces." Contemp. Math. 71 (1988): 237-262.

Hamilton, Richard S. "Three-manifolds with positive Ricci curvature." J. Differential Geom. 17, no. 2 (1982): 255-306.

Kenmotsu, Katsuei. "A class of almost contact Riemannian manifolds." Tôhoku Math. J. (2) 24 (1972): 93-103.

Nagaraja, H.G., D.L. Kiran Kumar and V.S. Prasad. "Ricci solitons on Kenmotsu manifolds under D-homothetic deformation." Khayyam J. Math. 4, no. 1 (2018): 102-109.

Nagaraja, H.G. and C.R. Premalatha. "Ricci solitons in Kenmotsu manifolds." J. Math. Anal. 3, no. 2 (2012): 18-24.

Tamássy, L. and T.Q. Binh. "On weakly symmetric and weakly projective symmetric Riemannian manifolds." Colloq. Math. Soc. János Bolyai 56 (1992): 663-670.

Tarafdar, M. and Mussa A.A. Jawarneh. "Semi-pseudo Ricci symmetric manifold." J. Indian Inst. Sci. 73, no. 6 (1993): 591-596.

Walker, A.G. "On Ruse’s spaces of recurrent curvature." Proc. London Math. Soc. (2) 52 (1950): 36-64.


Full Text: PDF

Download statistics: 737

Licencja Creative Commons
This article by Adara Monica Blaga, Kanak Kanti Baishya, Nihar Sarkar is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej