Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$

Yıl 2023, Cilt: 6 Sayı: 2, 117 - 127, 30.06.2023

Erol Kılıç , Mehmet Gülbahar , Ecem Kavuk , Esra Erkan

https://doi.org/10.33401/fujma.1277288

Öz

The necessary requirements for half-lightlike and coisotropic lightlike submanifolds to be a Ricci soliton are obtained. Some examples of Ricci soliton half-lightlike and Ricci soliton coisotropic lightlike submanifolds are given. The Ricci soliton equation is investigated on totally geodesic, totally umbilical, and irrotational lightlike submanifolds.

Anahtar Kelimeler

Concircular vector field, Concurrent vector field, Ricci soliton

Kaynakça

• [1] M. T. K. Abbassi, N. Amri, C. L. Bejan, Conformal vector fields and Ricci soliton structures on natural Riemann extensions, Mediterr. J. Math., 18(2) (2021), 1–16.
• [2] C. L. Bejan, M. Crasmareanu, Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global Anal. Geom., 46(2) (2014), 117–127.
• [3] A. M. Blaga, C. Özgür, Almost h-Ricci and almost h-Yamabe solitons with torse-forming potential vector field, Quaest. Math., 45(1) (2022), 143–163.
• [4] B. Y. Chen, S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19(1) (2014), 13–21.
• [5] S. Deshmukh, H. Alodan, H. Al-Sodais, A note on Ricci solitons, Balkan J. Geom. Appl., 16(1) (2011), 48–55.
• [6] S. Y. Perktaş, S. Keleş, Ricci solitons in 3-dimensional normal almost paracontact metric manifolds, Int. Electron. J. Geom., 8(2) (2015), 34–45.
• [7] A. Sardar, U. C. De, h-Ricci solitons on para-Kenmotsu manifolds, Differ. Geom. Dyn. Syst., 22 (2020), 218–228.
• [8] H. İ. Yoldaş, Ş. Eken Meriç, E. Yaşar, Some special vector fields on a cosymplectic manifold admitting a Ricci soliton, Miskolc Math. Notes, 22(2) (2021), 1039–1050.
• [9] K. Yano, On the torse-forming direction in Riemannian spaces, Proceedings of the Imperial Academy, 20(6) (1944), 340-345.
• [10] B. Y. Chen, Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc., 52(5) (2015), 1535–1547.
• [11] B. Y. Chen, Concircular vector fields and pseudo-Kaehler manifolds, Kragujevac J. Math., 40(1) (2016), 7–14.
• [12] B. Y. Chen, S. Deshmukh, Some results about concircular vector fields on Riemannian manifolds, Filomat, 34(3) (2020), 835–842.
• [13] S. Deshmukh, K. İlarslan, H. Alsodais, U. C. De, Spheres and Euclidean spaces via concircular vector fields, Mediterr. J. Math., 18(5) (2021), 1–14.
• [14] D. A. Kaya, L. Onat, Almost Ricci solitons and concircular vector fields, An. S¸ tiint¸. Univ. Al. I. Cuza Ias¸i. Mat. (N.S.), 64 (2018), 199-204.
• [15] S. Khan, A. Mahmood, A. T. Ali, Concircular vector fields for Kantowski-Sachs and Bianchi type-III spacetimes, Int. J. Geom. Methods Mod. Phys., 15(08) (2018), 1850126.
• [16] E. Kılıç, M. Gülbahar, E. Kavuk, Concurrent vector fields on lightlike hypersurfaces, Mathematics, 9(1) (2020), 59.
• [17] K. L. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Springer Dordrecht: Kluwer Academic Publishers, London, UK, 1996.
• [18] K. L. Duggal, A. Bejancu, Lightlike submanifolds of codimension two, Toyama Math. J., 15 (1992), 59–82.
• [19] K. L. Duggal, B. Şahin, Screen conformal half-lightlike submanifolds, Int. J. Math. Math. Sci., 2004(68) (2004), 3737–3753.
• [20] D. N. Kupeli, Singular Semi-Riemannian Geometry, Kluwer Academic, 1996.
• [21] K. L. Duggal, D. H. Jin, Totally umbilical lightlike submanifolds, Kodai Math. J., 26 (2003), 49-–68.
• [22] K. L. Duggal, B. Şahin, Differential Geometry of Lightlike Submanifolds, Springer Science, Business Media: Berlin, Germany, 2011.
• [23] K. L. Duggal, D. H. Jin, Half-lightlike submanifolds of codimension 2, Toyama Math. J., 22 (1999), 121–161.
• [24] D.H. Jin, Geometry of coisotropic submanifolds, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 8(1) (2001), 33—46.