**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

**Author(s):** Somashekhara Ganganna ^{a} , Bhavya Kenchalingaiah ^{b} , Shivaprasanna Godekere Shivakumar ^{c}

^{a}Department of Mathematics and Statiatics, M.S.Ramaiah University of Applied Sciences, Bengaluru-560058, India

^{b}Department of Mathematics, Presidency University, Bengaluru-560064, India

^{c}Department 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: shivaprasanna28@gmail.com)

**Full Text:** PDF

**Abstract**

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 connection

**References:**

- 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 (*, International Journal of Mathematics Trends and Technology*k*,*μ*) space forms**9**, 172–188, 2014. - K. Yano,
*On semi-symmetric metric connections*, Rev. Roumaine Math. Pures Appl.**15**, 1579–1586, 1970.