Title: Invariant submanifold of generalized Sasakian space form with semi-symmetric metric connection
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-21-00037; Volume 4 / Issue 1 / Year 2022, Pages 128-134
Document Type: Research Paper
aDepartment of Mathematics and Statiatics, M.S.Ramaiah University of Applied Sciences, Bengaluru-560058, India
bDepartment of Mathematics, Presidency University, Bengaluru-560064, India
cDepartment of Mathematics, Dr.Ambedkar institute of technology, Bengaluru-560056, India
Received: 27 May 2021, Accepted: 13 October 2021, Published: 20 January 2022.
Corresponding Author: Shivaprasanna Godekere Shivakumar (Email address: firstname.lastname@example.org)
Full Text: PDF
In this paper, we obtain necessary and sufficient condition for an Invariant submanifold of generalized Sasakian space form with semi-symmetric metric connections to be totally geodesic.
Keywords: Invariant submanifolds, generalized Sasakian space form, totally geodesic, semi-symmetric metric connectionReferences:
- P. Alegre and A. Carriazo, Structures on generalised Sasakian space forms, Diff. Geo. and its Application 26, 656–666, 2008.
- P. Alegre and A. Carriazo, Submanifolds of generalised Sasakian space forms, Taiwanese J. Math. 13, 923–941, 2009.
- P. Alegre and A. Carriazo, Generalised Sasakian space forms and conformal changes of the metric, Results in Math. 59, 485–493, 2011.
- A. Carriazo, On generalised Sasakian space forms, Proceedings of the Ninth International Workshop on Diff. Geo. 9, 31–39, 2005.
- U. Chand De and A. Haseeb, On generalized Sasakian-space-forms with M-projective curvature tensor, Adv. Pure Appl. Math. 9 (1), 67–73, 2018.
- B. Y. Chen, Some pinching and classification theorems for minimal submanifolds, Arch. Math. (Basel) 60 (6), 568–578, 1993.
- B. Y. Chen, Strings of Riemannian invariants, inequalities, ideal immersions and their applications, The Third Pacific Rim Geometry Conference (Seoul, 1996), 7-60, Monogr. Geom. Topology, 25, Int. Press, Cambridge, MA, 1998.
- B. Y. Chen, δ-invariants, inequalities of submanifolds and their applications, in topics in differential geometry, Eds. A. Mihai, I. Mihai, R. Miron, Editura Academiei Romane, Bucuresti, 29–156, 2008.
- H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34, 27–50, 1932.
- A. A. Hosseinzadeh, Some curvature properties of generalized Sasakianspace-forms, Proc. Nat. Acad. Sci. India Sect. A 89 (4), 721–727, 2019.
- S. K. Hui, S. Uddin, A. H. Alkhaldi and P. Mandal, Invariant submanifolds of generalized Sasakian-space-forms, Int. J. of Geom. Methods in Modern Physics 15, 1–21, 2018.
- S. K. Hui and J. Roy, Invariant and anti-invariant submanifolds of special quasi-Sasakian manifolds, Journal of Geometry 109 (2), 2018.
- S. K. Hui, P. Mandal and S. Kishor,Submanifolds of generalized Sasakian- space-forms with respect to certain connections, Int. J. Math. and Appl. 6 (3), 285–294, 2018.
- T. Imai, Notes on semi-symmetric metric connection, Vol. I. Tensor (N.S.) 24, 293–296, 1972.
- Y. B. Maralabhavi and G. S. Shivaprasanna, Second order parallel tensors on generalized Sasakian spaceforms, International Journal of Mathematical Engineering and Science 1, 11–21, 2012.
- Z. Nakao, Submanifolds of a Riemannian manifold with semi-symmetric metric connection, Proc. Amer. Math. Soc. 54, 261–266, 1976.
- D. G. Prakasha and H. G. Nagaraja, On quasi-conformally at and quasiconformally semisymmetric generalized Sasakian-space-forms, CUBO A Mathematical Journal 15 (3), 59–70, 2013.
- G. S. Shivaprasanna, Y. B. Maralabhavi and G. Somashekhara, On semi-symmetric connection in a generalized (k, μ) space forms, International Journal of Mathematics Trends and Technology 9, 172–188, 2014.
- K. Yano, On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15, 1579–1586, 1970.