Invariant Submanifolds of Sasakian Manifolds Admitting Semisymmetric Nonmetric Connection. (9th August 2012)

• Record Type: Journal Article
• Authors: Anitha, B. S.; Bagewadi, C. S.
• Other Names: Khalilov V. R. Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2012(2012)
• Publication Date: 2012-08-09
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2012/947640
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : The object of this paper is to study invariant submanifolds M of Sasakian manifolds M ˜ admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms σ and σ ¯ with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental form σ is recurrent, 2-recurrent, generalized 2-recurrent, semiparallel, pseudoparallel, and Ricci-generalized pseudoparallel and M has parallel third fundamental form with respect to semisymmetric nonmetric connection, then M is totally geodesic with respect to Levi-Civita connection.