ON f-KENMOTSU MANIFOLDS AND THEIR SUBMANIFOLDS WITH QUARTER SYMMETRIC METRIC CONNECTIONS

Avijit Sarkar, Nirmal Biswas

DOI Number
https://doi.org/10.22190/FUMI2004017S
First page
1017
Last page
1030

Abstract


The object of the present paper is to study invariant submanifolds of f-Kenmotsu manifolds with respect to quarter symmetric metric connections. Some necessary and sufficient conditions for such submanifolds to be totally geodesic have been deduced. Also we construct an example of a submanifold of a five-dimensional f-Kenmotsu manifold to justify our results.

Keywords

f-Kenmotsu manifold; quarter symmetric metric connection.

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References


Asperti, A. C., Lobos, G. A. and Mercuri, F., Pseudo-parallel immersions in space forms, Mat. Contemp., 17(1999), 53-70.

Asperti, A. C., Lobos, G. A. and Mercuri, F., Pseudo-parallel submanifolds of a space forms, Adv. Geom. 2(2002), 57-71.

Biswas, S. C. and De, U. C., Quarter-symmetric metric connection in an SP-Sasakian manifold, Commun. Fac. Sci. Univ. Ank. Series, 46(1997), 49-56.

Calin, C. and Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bulletin of the Malaysian Mathematical Sciences Society, 33(2010), 361–368.

Chen, B. Y., Geometry of submanifolds, Maecel Dekker Inc., New York (1973).

Demirli, T., Ekici, C. and Gorgulu, A., Ricci solitons in f-Kenmotsu manifolds with the semisymmetric non-metric connection, New Trends in Mathematical Sci., 4(2016), 276-284.

De, U. C., Zhao, P., Mandal, K. and Han, Y., Certain conditions on P-Sasakian manifolds admitting a quarter-symmetric metric connection, Chin. Ann. Math. Ser. B, 41(2020), 133-146.

De, U. C. and Majhi, P., On invariant submanifolds of Kenmotsu manifolds, J. Geom., 106(2015), 109-122.

Deszcz, R., On pesudosymmetric spaces, Bull. Soc. Belg. Math. Ser A, 44(1992), 1-34.

Friedman, A. and Schouten, J. A., Uber die geometric derhalbsymmetrischen Ubertragung, Math. Zeitscr., 21(1924), 211-223.

Golab, S., On a semi-symmetric and quarter symmetric linear connections, Tensor, N. S., 29(1975), 249-254.

Hu, Chaogui. and Wang, Yaning., A note on invariant Submanifolds of trans-Sasakian manifolds, Int. Ele. J. of Geom., 9(2016), 27-35.

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

Kon, M., Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Repors, 25(1973), 330-336.

Lumiste, U., Semiparallel submanifolds in space forms, Springer Science + Business Media, LLC, 2009, DOI: 10.1007/978-0-387-49913-0.

Mishra, R. S. and Pandey, S. N., On quarter-symmetric metric F-connections, Tensor, N.S., 34(1980), 1-7.

Mondal, A. K., and De, U. C., Some properties of a quarter-symmetric connection on a Sasakian manifold, Bull of Math. Anal. and Appl., 3(2009), 99-108.

Mukhopadhyay, S., Roy, A. K. and Barua, B., Some properties of a quarter-symmetric metric connection on a Riemannian manifold, Soochow J. of Math., 17(1991), 205-211.

Murathan, C., Arslan, K. and Ezentas, E., Ricci generalizespseudo-symmetric immersions, Differential geometry and its applications, Matfyzpress, Prague, 99–108(2005).

Ozgur, C. and Murathan, C.,On invariant submanifolds of Lorentzian Para-Sasakian manifolds, Arab. J. Sci. Eng., 34(2008), 177-185.

Ozgur, C., Sular, S. and Murathan, C.,On pseudoparallel invariant submanifolds of contact metric manifolds, Bull. Transilv Univ. Brasov Ser. B(N.S), 14(2007), 227-234.

Olszak, Z., Rosca, R., Normal locally conformal almost cosymplectic manifolds, Publicationes Mathematicae Debrecen, 39(1991), 315-323.

Roter, W., On conformally recurrent Ricci-recurrent manifolds, Colloq Math., 46(1982), 45-57. [24] Sarkar, A., Biswas, N. and Sen, M., On some submanifolds of ()-LP-Sasakian manifolds, Acta Univ. Apu., 61(2020), 65-80.




DOI: https://doi.org/10.22190/FUMI2004017S

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