Five-Dimensional Contact CR -Submanifolds in S 7 ( 1 )

Mirjana Djorić and Marian Ioan Munteanu
Additional contact information
Mirjana Djorić: Faculty of Mathematics, University of Belgrade, Studentski trg 16, pp. 550, 11000 Belgrade, Serbia
Marian Ioan Munteanu: Faculty of Mathematics, Alexandru Ioan Cuza University of Iasi, Bd. Carol I, no. 11, 700506 Iasi, Romania

Mathematics, 2020, vol. 8, issue 8, 1-24

Abstract: Due to the remarkable property of the seven-dimensional unit sphere to be a Sasakian manifold with the almost contact structure ( φ , ξ , η ) , we study its five-dimensional contact C R -submanifolds, which are the analogue of C R -submanifolds in (almost) Kählerian manifolds. In the case when the structure vector field ξ is tangent to M , the tangent bundle of contact C R -submanifold M can be decomposed as T ( M ) = H ( M ) ⊕ E ( M ) ⊕ R ξ , where H ( M ) is invariant and E ( M ) is anti-invariant with respect to φ . On this occasion we obtain a complete classification of five-dimensional proper contact C R -submanifolds in S 7 ( 1 ) whose second fundamental form restricted to H ( M ) and E ( M ) vanishes identically and we prove that they can be decomposed as (multiply) warped products of spheres.

Keywords: contact CR -submanifold; nearly totally geodesic submanifold; warped product; seven-dimensional unit sphere (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/8/1278/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/8/1278/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:8:p:1278-:d:393927

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().