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Year 2024, Early Access, 1 - 15

Jae Won Lee Majid Ali Choudhary Aliya Naaz Sıddıquı

Abstract

References

  • [1] M. Aslam and A.N. Siddiqui, Bounds for generalized normalized -Casorati curvature for submanifold in real space forms endowed with a quarter-symmetric connection, Balkan J. Geom. Appl., 27(2), 1-12, 2022.
  • [2] O. Bahadır and S. Uddin, Slant submanifolds of Golden Riemannian manifolds, Journal of Mathematical Extension 13 (4), 2019.
  • [3] D. Blair, Quasi-umbilical, minimal submanifolds of Euclidean space, Simon Stevin, 51, 3-22, 1977.
  • [4] B.Y. Chen, Some pinching and classification theorems for minimal submanifolds, Arch. Math. 60, 568-578, 1993.
  • [5] M. Crasmareanu and C. Hretcanu, Golden differential geometry, Chaos Solitons Fractals, 38 (5), 1229-1238, 2008.
  • [6] S. Decu, S. Haesen and L. Verstraelen, Optimal inequalities involving Casorati curvatures, Bull. Transylv. Univ. Bra¸sov, Ser. B 14(49), suppl., 85-93, 2007.
  • [7] S. Decu, S. Haesen and L. Verstraelen, Optimal inequalities characterising quasi-umbilical submanifolds, J. Inequal. Pure Appl. Math. 9(3), Article ID 79, 2008.
  • [8] A. Friedmann and A. Schouten, Uber die Geometrie der halbsymmetrischen Ubertragungen, Mathematische Zeitschrift 21, 211-223, 1924.
  • [9] A. Gezer, N. Cengiz and A. Salimov, On integrability of Golden Riemannian structures, Turkish J. Math. 37, 693-703, 2013.
  • [10] V. Ghisoiu, Inequalities for the Casorati curvatures of slant submanifolds in complex space forms, In: Riemannian Geometry and Applications. Proceedings RIGA 2011, Ed. Univ. Bucure¸sti, Bucharest 145-150, 2011.
  • [11] S.I. Goldberg and K. Yano, Polynomial structures on manifolds, Kodai Math. Sem. Rep. 22, 199-218, 1970.
  • [12] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34, 27-50, 1932.
  • [13] C. Hretcanu and M. Crasmareanu, On some invariant submanifolds in a Riemannian manifold with golden structure, An. Stiins. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 53, 199-211, 2007.
  • [14] C. Hretcanu and M. Crasmareanu, Applications of the golden ratio on Riemannian manifolds, Turkish J. Math. 33, 179-191, 2009.
  • [15] T. Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor(N.S.), 23, 300-306, 1972.
  • [16] T. Imai, Notes on semi-symmetric metric connection, Tensor(N.S.), 24, 293-296, 1972.
  • [17] C.W. Lee, D.W. Yoon and J.W. Lee, Optimal inequalities for the Casorati curvatures of submanifolds of real space forms endowed with semi-symmetric metric connections, J. Inequal. Appl. 2014:327, 9 pp. MR 3344114, 2014.
  • [18] C.W. Lee, J.W. Lee and G.E. Vilcu, Optimal inequalities for the normalized $\delta$-Casorati curvatures of submanifolds in Kenmotsu space forms, Advances in Geom. 17, 2017.
  • [19] J.W. Lee and G.E. Vilcu, Inequalities for generalized normalized Casorati curvatures of slant submanifolds in quaternion space forms, Taiwanese J. Math. 19, 691-702, 2015.
  • [20] C.W. Lee, J.W. Lee, G.E. Vilcu, and D.W. Yoon, Optimal Inequalities for the Casorati curvatures of submanifolds of generalized space forms endowed with semi-symmetric metric connections, Bull. Korean Math. Soc. 52, 1631–1647, 2015.
  • [21] X. Liu, On Ricci curvature of totally real submanifolds in a quaternion projective space, Arch. Math. 38 (4), 297-305, 2002.
  • [22] X. Liu and W. Dai, Ricci curvature of submanifolds in a quaternion projective space, Commun. Korean Math. Soc. 17 (4), 625-633, 2002.
  • [23] A. Mihai and C. Ozgur, Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection, Taiwanese J. Math. 14, 1465-1477, 2010.
  • [24] A. Mihai and C. Ozgur, Chen inequalities for submanifolds of complex space forms and Sasakian space forms endowed with semi-symmetric metric connection, Rocky Mountain J. Math., 41, 1653-1673, 2011.
  • [25] I. Mihai, F.R. Al-Solamy and M.H. Shahid, On Ricci curvature of a quaternion CR-submanifold in a quaternion space form, Rad. Mat. 12 (1), 91-98, 2003.
  • [26] Z. Nakao, Submanifolds of a Riemannian manifold with semi-symmetric metric connections, Proc. Amer. Math. Soc. 54, 261-266, 1976.
  • [27] T. Oprea, Optimization methods on Riemannian submanifolds, An. Univ. Bucuresti Math. 54, 127-136, 2005.
  • [28] M. Ozkan, Prolongations of golden structures to tangent bundles, Differential Geometry- Dynamical Sytem. 16, 227-23, 2014.
  • [29] N.O. Poyraz and Y. Erol, Lightlike Hypersurfaces of a Golden Semi-Riemannian Manifold, Mediterr. J. Math. 14:204, DOI 10.1007/s00009-017-0999-2, 2017.
  • [30] S.S. Shukla and P.K. Rao, Ricci curvature of quaternion slant submanifolds in quaternion space forms, Acta Math. Acad. Paedagog. Nyházi 28(1), 69-81, 2012.
  • [31] A.N. Siddiqui, Upper bound inequalities for $\delta$-Casorati curvatures of submanifolds in generalized Sasakian space forms admitting a semi-symmetric metric connection, Inter. Elec. J. Geom. 11(1), 57-67, 2018.
  • [32] M.M. Tripathi, Inequalities for algebraic Casorati curvatures and their applications, arXiv:1607.05828v1 [math.DG] 20 Jul 2016.
  • [33] G.E. Vilcu, On Chen invariant and inequalities in quaternionic geometry, J. Inequal. Appl. 2013, Article ID 66, 2013
  • [34] K. Yano, On semi-symmetric metric connection, Rev. roumaine Math. Pure Appl. 15, 1579-1586, 1970.
  • [35] P. Zhang, L. Zhang and W. Song, Inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, Taiwanese J. Math. 18, 1841-1862, 2014.

Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection

Year 2024, Early Access, 1 - 15

Jae Won Lee Majid Ali Choudhary Aliya Naaz Sıddıquı

Abstract

In this article, we derive some sharp inequalities for slant submanifolds immersed into golden Riemannian space forms with a semi-symmetric metric connection. Also, we characterize submanifolds for the case of equalities. Lastly, we discuss these inequalities for some special submanifolds.

Keywords

Golden Riemannian manifolds $\delta$-Casorati curvature Slant submanifolds

References

  • [1] M. Aslam and A.N. Siddiqui, Bounds for generalized normalized -Casorati curvature for submanifold in real space forms endowed with a quarter-symmetric connection, Balkan J. Geom. Appl., 27(2), 1-12, 2022.
  • [2] O. Bahadır and S. Uddin, Slant submanifolds of Golden Riemannian manifolds, Journal of Mathematical Extension 13 (4), 2019.
  • [3] D. Blair, Quasi-umbilical, minimal submanifolds of Euclidean space, Simon Stevin, 51, 3-22, 1977.
  • [4] B.Y. Chen, Some pinching and classification theorems for minimal submanifolds, Arch. Math. 60, 568-578, 1993.
  • [5] M. Crasmareanu and C. Hretcanu, Golden differential geometry, Chaos Solitons Fractals, 38 (5), 1229-1238, 2008.
  • [6] S. Decu, S. Haesen and L. Verstraelen, Optimal inequalities involving Casorati curvatures, Bull. Transylv. Univ. Bra¸sov, Ser. B 14(49), suppl., 85-93, 2007.
  • [7] S. Decu, S. Haesen and L. Verstraelen, Optimal inequalities characterising quasi-umbilical submanifolds, J. Inequal. Pure Appl. Math. 9(3), Article ID 79, 2008.
  • [8] A. Friedmann and A. Schouten, Uber die Geometrie der halbsymmetrischen Ubertragungen, Mathematische Zeitschrift 21, 211-223, 1924.
  • [9] A. Gezer, N. Cengiz and A. Salimov, On integrability of Golden Riemannian structures, Turkish J. Math. 37, 693-703, 2013.
  • [10] V. Ghisoiu, Inequalities for the Casorati curvatures of slant submanifolds in complex space forms, In: Riemannian Geometry and Applications. Proceedings RIGA 2011, Ed. Univ. Bucure¸sti, Bucharest 145-150, 2011.
  • [11] S.I. Goldberg and K. Yano, Polynomial structures on manifolds, Kodai Math. Sem. Rep. 22, 199-218, 1970.
  • [12] H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34, 27-50, 1932.
  • [13] C. Hretcanu and M. Crasmareanu, On some invariant submanifolds in a Riemannian manifold with golden structure, An. Stiins. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 53, 199-211, 2007.
  • [14] C. Hretcanu and M. Crasmareanu, Applications of the golden ratio on Riemannian manifolds, Turkish J. Math. 33, 179-191, 2009.
  • [15] T. Imai, Hypersurfaces of a Riemannian manifold with semi-symmetric metric connection, Tensor(N.S.), 23, 300-306, 1972.
  • [16] T. Imai, Notes on semi-symmetric metric connection, Tensor(N.S.), 24, 293-296, 1972.
  • [17] C.W. Lee, D.W. Yoon and J.W. Lee, Optimal inequalities for the Casorati curvatures of submanifolds of real space forms endowed with semi-symmetric metric connections, J. Inequal. Appl. 2014:327, 9 pp. MR 3344114, 2014.
  • [18] C.W. Lee, J.W. Lee and G.E. Vilcu, Optimal inequalities for the normalized $\delta$-Casorati curvatures of submanifolds in Kenmotsu space forms, Advances in Geom. 17, 2017.
  • [19] J.W. Lee and G.E. Vilcu, Inequalities for generalized normalized Casorati curvatures of slant submanifolds in quaternion space forms, Taiwanese J. Math. 19, 691-702, 2015.
  • [20] C.W. Lee, J.W. Lee, G.E. Vilcu, and D.W. Yoon, Optimal Inequalities for the Casorati curvatures of submanifolds of generalized space forms endowed with semi-symmetric metric connections, Bull. Korean Math. Soc. 52, 1631–1647, 2015.
  • [21] X. Liu, On Ricci curvature of totally real submanifolds in a quaternion projective space, Arch. Math. 38 (4), 297-305, 2002.
  • [22] X. Liu and W. Dai, Ricci curvature of submanifolds in a quaternion projective space, Commun. Korean Math. Soc. 17 (4), 625-633, 2002.
  • [23] A. Mihai and C. Ozgur, Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection, Taiwanese J. Math. 14, 1465-1477, 2010.
  • [24] A. Mihai and C. Ozgur, Chen inequalities for submanifolds of complex space forms and Sasakian space forms endowed with semi-symmetric metric connection, Rocky Mountain J. Math., 41, 1653-1673, 2011.
  • [25] I. Mihai, F.R. Al-Solamy and M.H. Shahid, On Ricci curvature of a quaternion CR-submanifold in a quaternion space form, Rad. Mat. 12 (1), 91-98, 2003.
  • [26] Z. Nakao, Submanifolds of a Riemannian manifold with semi-symmetric metric connections, Proc. Amer. Math. Soc. 54, 261-266, 1976.
  • [27] T. Oprea, Optimization methods on Riemannian submanifolds, An. Univ. Bucuresti Math. 54, 127-136, 2005.
  • [28] M. Ozkan, Prolongations of golden structures to tangent bundles, Differential Geometry- Dynamical Sytem. 16, 227-23, 2014.
  • [29] N.O. Poyraz and Y. Erol, Lightlike Hypersurfaces of a Golden Semi-Riemannian Manifold, Mediterr. J. Math. 14:204, DOI 10.1007/s00009-017-0999-2, 2017.
  • [30] S.S. Shukla and P.K. Rao, Ricci curvature of quaternion slant submanifolds in quaternion space forms, Acta Math. Acad. Paedagog. Nyházi 28(1), 69-81, 2012.
  • [31] A.N. Siddiqui, Upper bound inequalities for $\delta$-Casorati curvatures of submanifolds in generalized Sasakian space forms admitting a semi-symmetric metric connection, Inter. Elec. J. Geom. 11(1), 57-67, 2018.
  • [32] M.M. Tripathi, Inequalities for algebraic Casorati curvatures and their applications, arXiv:1607.05828v1 [math.DG] 20 Jul 2016.
  • [33] G.E. Vilcu, On Chen invariant and inequalities in quaternionic geometry, J. Inequal. Appl. 2013, Article ID 66, 2013
  • [34] K. Yano, On semi-symmetric metric connection, Rev. roumaine Math. Pure Appl. 15, 1579-1586, 1970.
  • [35] P. Zhang, L. Zhang and W. Song, Inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, Taiwanese J. Math. 18, 1841-1862, 2014.
There are 35 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Jae Won Lee 0000-0001-8562-0767

Majid Ali Choudhary 0000-0001-5920-1227

Aliya Naaz Sıddıquı 0000-0003-3895-7548

Early Pub Date January 10, 2024
Publication Date
Published in Issue Year 2024 Early Access

Cite

APA Lee, J. W., Choudhary, M. A., & Sıddıquı, A. N. (2024). Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection. Hacettepe Journal of Mathematics and Statistics1-15. https://doi.org/10.15672/hujms.1152136
AMA Lee JW, Choudhary MA, Sıddıquı AN. Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection. Hacettepe Journal of Mathematics and Statistics. Published online January 1, 2024:1-15. doi:10.15672/hujms.1152136
Chicago Lee, Jae Won, Majid Ali Choudhary, and Aliya Naaz Sıddıquı. “Some Bounds for Casorati Curvatures on Golden Riemannian Space Forms With SSM Connection”. Hacettepe Journal of Mathematics and Statistics, January (January 2024), 1-15. https://doi.org/10.15672/hujms.1152136.
EndNote Lee JW, Choudhary MA, Sıddıquı AN (January 1, 2024) Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection. Hacettepe Journal of Mathematics and Statistics 1–15.
IEEE J. W. Lee, M. A. Choudhary, and A. N. Sıddıquı, “Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection”, Hacettepe Journal of Mathematics and Statistics, pp. 1–15, January 2024, doi: 10.15672/hujms.1152136.
ISNAD Lee, Jae Won et al. “Some Bounds for Casorati Curvatures on Golden Riemannian Space Forms With SSM Connection”. Hacettepe Journal of Mathematics and Statistics. January 2024. 1-15. https://doi.org/10.15672/hujms.1152136.
JAMA Lee JW, Choudhary MA, Sıddıquı AN. Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection. Hacettepe Journal of Mathematics and Statistics. 2024;:1–15.
MLA Lee, Jae Won et al. “Some Bounds for Casorati Curvatures on Golden Riemannian Space Forms With SSM Connection”. Hacettepe Journal of Mathematics and Statistics, 2024, pp. 1-15, doi:10.15672/hujms.1152136.
Vancouver Lee JW, Choudhary MA, Sıddıquı AN. Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection. Hacettepe Journal of Mathematics and Statistics. 2024:1-15.

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