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Year 2023, Volume: 6 Issue: 2, 117 - 127, 30.06.2023

Erol Kılıç Mehmet Gülbahar Ecem Kavuk Esra Erkan

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

Abstract

References

  • [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.

Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$

Year 2023, Volume: 6 Issue: 2, 117 - 127, 30.06.2023

Erol Kılıç Mehmet Gülbahar Ecem Kavuk Esra Erkan

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

Abstract

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.

Keywords

Concircular vector field Concurrent vector field Ricci soliton

References

  • [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.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Erol Kılıç 0000-0001-7536-0404

Mehmet Gülbahar 0000-0001-6950-7633

Ecem Kavuk 0000-0002-8922-2691

Esra Erkan 0000-0003-0456-6418

Early Pub Date June 11, 2023
Publication Date June 30, 2023
Submission Date April 4, 2023
Acceptance Date June 1, 2023
Published in Issue Year 2023 Volume: 6 Issue: 2

Cite

APA Kılıç, E., Gülbahar, M., Kavuk, E., Erkan, E. (2023). Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$. Fundamental Journal of Mathematics and Applications, 6(2), 117-127. https://doi.org/10.33401/fujma.1277288
AMA Kılıç E, Gülbahar M, Kavuk E, Erkan E. Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$. FUJMA. June 2023;6(2):117-127. doi:10.33401/fujma.1277288
Chicago Kılıç, Erol, Mehmet Gülbahar, Ecem Kavuk, and Esra Erkan. “Ricci Soliton Lightlike Submanifolds With Co-Dimension $2$”. Fundamental Journal of Mathematics and Applications 6, no. 2 (June 2023): 117-27. https://doi.org/10.33401/fujma.1277288.
EndNote Kılıç E, Gülbahar M, Kavuk E, Erkan E (June 1, 2023) Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$. Fundamental Journal of Mathematics and Applications 6 2 117–127.
IEEE E. Kılıç, M. Gülbahar, E. Kavuk, and E. Erkan, “Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$”, FUJMA, vol. 6, no. 2, pp. 117–127, 2023, doi: 10.33401/fujma.1277288.
ISNAD Kılıç, Erol et al. “Ricci Soliton Lightlike Submanifolds With Co-Dimension $2$”. Fundamental Journal of Mathematics and Applications 6/2 (June 2023), 117-127. https://doi.org/10.33401/fujma.1277288.
JAMA Kılıç E, Gülbahar M, Kavuk E, Erkan E. Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$. FUJMA. 2023;6:117–127.
MLA Kılıç, Erol et al. “Ricci Soliton Lightlike Submanifolds With Co-Dimension $2$”. Fundamental Journal of Mathematics and Applications, vol. 6, no. 2, 2023, pp. 117-2, doi:10.33401/fujma.1277288.
Vancouver Kılıç E, Gülbahar M, Kavuk E, Erkan E. Ricci Soliton Lightlike Submanifolds with Co-Dimension $2$. FUJMA. 2023;6(2):117-2.
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