Abstract
Chen (2001) initiated the study of CR-warped product submanifolds in Kaehler manifolds and established a general inequality between an intrinsic invariant (the warping function) and an extrinsic invariant (second fundamental form).In this paper, we establish a relationship for the squared norm of the second fundamental form (an extrinsic invariant) of warped product bi-slant submanifolds of Kenmotsu manifolds in terms of the warping function (an intrinsic invariant) and bi-slant angles. The equality case is also considered. Some applications of derived inequality are given.
Highlights
Chen as a CR-warped product submanifold of Kaehler manifolds in his series of articles [11,12]
We study warped product bi-slant submanifolds of a Kenmotsu manifold
From (1.4), (2.1) and (3.1), the second case is trivial i.e., there does not exist any proper warped product bi-slant submanifold of a Kenmotsu manifold when the structure vector field is tangent to the fiber
Summary
Kenmotsu studied one class of almost contact metric manifolds known as Kenmotsu manifolds. He proved that: Arab Journal of Mathematical Sciences Vol 27 No 1, 2021 pp. Published in the Arab Journal of Mathematical Sciences. The publisher wishes to inform readers that the article “On warped product bi-slant submanifolds of Kenmotsu manifolds” was originally published by the previous publisher of the Arab Journal of Mathematical Sciences and the pagination of this article has been subsequently changed. There has been no change to the content of the article This change was necessary for the journal to transition from the previous publisher to the new one. (2019), “On warped product bi-slant submanifolds of Kenmotsu manifolds”, Arab Journal of Mathematical Sciences, Vol 27 No 1, pp. A ð2m þ 1Þ-dimensional manifold M~ is said to be an almost contact manifold if it admits an endomorphism w of its tangent bundle TM~ , a vector field ξ and a 1-form η, which satisfy: w2 1⁄4 −I þ η ⊗ ξ; wξ 1⁄4 0; ηðξÞ 1⁄4 0; η+w 1⁄4 0:
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
