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http://dx.doi.org/10.4134/CKMS.c180446

CERTAIN RESULTS ON CONTACT METRIC GENERALIZED (κ, µ)-SPACE FORMS  

Huchchappa, Aruna Kumara (Department of Mathematics Kuvempu University)
Naik, Devaraja Mallesha (Department of Mathematics Kuvempu University)
Venkatesha, Venkatesha (Department of Mathematics Kuvempu University)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.4, 2019 , pp. 1315-1328 More about this Journal
Abstract
The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.
Keywords
generalized (${\kappa}$, ${\mu}$)-space forms; Sasakian manifold; ${\ast}$-Ricci soliton; gradient ${\ast}$-Ricci soliton;
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1 G. Kaimakamis and K. Panagiotidou, *-Ricci solitons of real hypersurfaces in non-flat complex space forms, J. Geom. Phys. 86 (2014), 408-413. https://doi.org/10.1016/j.geomphys.2014.09.004   DOI
2 U. K. Kim, Conformally at generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note Mat. 26 (2006), no. 1, 55-67.
3 M. Kon, Invariant submanifolds in Sasakian manifolds, Math. Ann. 219 (1976), no. 3, 277-290. https://doi.org/10.1007/BF01354288   DOI
4 T. Koufogiorgos, Contact Riemannian manifolds with constant $\phi$-sectional curvature, Tokyo J. Math. 20 (1997), no. 1, 13-22. https://doi.org/10.3836/tjm/1270042394   DOI
5 T. Koufogiorgos and C. Tsichlias, On the existence of a new class of contact metric manifolds, Canad. Math. Bull. 43 (2000), no. 4, 440-447. https://doi.org/10.4153/CMB-2000-052-6   DOI
6 T. Koufogiorgos and C. Tsichlias, Generalized (k, $\mu$)-contact metric manifolds with llgrad kll = constant, J. Geom. 78 (2003), no. 1-2, 83-91. https://doi.org/10.1007/s00022-003-1678-y   DOI
7 D. G. Prakasha, S. K. Hui, and K. Mirji, On 3-dimensional contact metric generalized (k, $\mu$)-space forms, Int. J. Math. Math. Sci. (2014), Art. ID 797162, 6 pp. https://doi.org/10.1155/2014/797162   DOI
8 C. R. Premalatha and H. G. Nagaraja, Recurrent generalized (k, $\mu$) space forms, Acta Univ. Apulensis Math. Inform. No. 38 (2014), 95-108.
9 P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math. 141 (2004), 157-183. https://doi.org/10.1007/BF02772217   DOI
10 P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian space forms, Taiwanese J. Math. 13 (2009), no. 3, 923-941. https://doi.org/10.11650/twjm/1500405448   DOI
11 P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal changes of the metric, Results Math. 59 (2011), no. 3-4, 485-493. https://doi.org/10.1007/s00025-011-0115-z   DOI
12 M. Belkhelfa, R. Deszcz, and L. Verstraelen, Symmetry properties of Sasakian space forms, Soochow J. Math. 31 (2005), no. 4, 611-616.
13 A. Sarkar, U. C. De, and M. Sen, Some results on generalized (k, $\mu$)-contact metric manifolds, Acta Univ. Apulensis Math. Inform. No. 32 (2012), 49-59.
14 A. A. Shaikh, K. Arslan, C. Murathan, and K. K. Baishya, On 3-dimensional generalized (k, $\mu$)-contact metric manifolds, Balkan J. Geom. Appl. 12 (2007), no. 1, 122-134.
15 B. Shanmukha, Venkatesha, and S. V. Vishunuvardhana, Some results on generalized (k, $\mu$)-space forms, NTMSCI. 6 (2018), no. 3, 48-56.
16 R. Sharma, Certain results on K-contact and (k, $\mu$)-contact manifolds, J. Geom. 89 (2008), no. 1-2, 138-147. https://doi.org/10.1007/s00022-008-2004-5   DOI
17 S. Sular and C. Ozgur, Generalized Sasakian space forms with semi-symmetric nonmetric connections, Proc. Est. Acad. Sci. 60 (2011), no. 4, 251-257. https://doi.org/10.3176/proc.2011.4.05   DOI
18 S. Tachibana, On almost-analytic vectors in almost-Kahlerian manifolds, Tohoku Math. J. (2) 11 (1959), 247-265. https://doi.org/10.2748/tmj/1178244584   DOI
19 Venkatesha and B. Shanmukha, $W_2$-curvature tensor on generalized Sasakian space forms, Cubo 20 (2018), no. 1, 17-29. https://doi.org/10.4067/s0719-06462018000100017   DOI
20 D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976.
21 D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, MA, 2002. https://doi.org/10.1007/978-1-4757-3604-5
22 D. E. Blair, T. Koufogiorgos, and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), no. 1-3, 189-214. https://doi.org/10.1007/BF02761646   DOI
23 C. Calin and M. Crasmareanu, From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 3, 361-368.
24 A. Carriazo, V. Martin Molina, and M. M. Tripathi, Generalized (k, $\mu$)-space forms, Mediterr. J. Math. 10 (2013), no. 1, 475-496. https://doi.org/10.1007/s00009-012-0196-2   DOI
25 U. C. De and K. Mandal, Certain results on generalized (k, $\mu$)-contact metric manifolds, J. Geom. 108 (2017), no. 2, 611-621. https://doi.org/10.1007/s00022-016-0362-y   DOI
26 A. Ghosh, Certain contact metrics as Ricci almost solitons, Results Math. 65 (2014), no. 1-2, 81-94. https://doi.org/10.1007/s00025-013-0331-9   DOI
27 S. Ghosh and U. C. De, On a class of generalized (k, $\mu$)-contact metric manifolds, Jangjeon Math Soc. 13 (2010), 337-347.
28 A. Ghosh and D. S. Patra, *-Ricci soliton within the frame-work of Sasakian and (k, $\mu$)-contact manifold, Int. J. Geom. Methods Mod. Phys. 15 (2018), no. 7, 1850120, 21 pp. https://doi.org/10.1142/S0219887818501207   DOI
29 T. Hamada, Real hypersurfaces of complex space forms in terms of Ricci *-tensor, Tokyo J. Math. 25 (2002), no. 2, 473-483. https://doi.org/10.3836/tjm/1244208866   DOI
30 T. Hamada and J.-I. Inoguchi, Real hypersurfaces of complex space forms with symmetric Ricci *-tensor, Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math. Sci. 38 (2005), 1-5.
31 S. K. Hui, S. Uddin, and P. Mandal, Submanifolds of generalized (k, $\mu$)-space-forms, Period. Math. Hungar. 77 (2018), no. 2, 329-339. https://doi.org/10.1007/s10998-018-0248-x   DOI