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Open AccessArticle

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

1
Faculty of Mathematics, University of Belgrade, Studentski trg 16, pp. 550, 11000 Belgrade, Serbia
2
Faculty of Mathematics, Alexandru Ioan Cuza University of Iasi, Bd. Carol I, no. 11, 700506 Iasi, Romania
*
Author to whom correspondence should be addressed.
Dedicated to the memory of Professor Aurel Bejancu.
Mathematics 2020, 8(8), 1278; https://doi.org/10.3390/math8081278
Received: 8 July 2020 / Revised: 25 July 2020 / Accepted: 27 July 2020 / Published: 3 August 2020
(This article belongs to the Special Issue Riemannian Geometry of Submanifolds)
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 CR-submanifolds, which are the analogue of CR-submanifolds in (almost) Kählerian manifolds. In the case when the structure vector field ξ is tangent to M, the tangent bundle of contact CR-submanifold M can be decomposed as T(M)=H(M)E(M)Rξ, 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 CR-submanifolds in S7(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. View Full-Text
Keywords: contact CR-submanifold; nearly totally geodesic submanifold; warped product; seven-dimensional unit sphere contact CR-submanifold; nearly totally geodesic submanifold; warped product; seven-dimensional unit sphere
MDPI and ACS Style

Djorić, M.; Munteanu, M.I. Five-Dimensional Contact CR-Submanifolds in S 7 ( 1 ) . Mathematics 2020, 8, 1278. https://doi.org/10.3390/math8081278

AMA Style

Djorić M, Munteanu MI. Five-Dimensional Contact CR-Submanifolds in S 7 ( 1 ) . Mathematics. 2020; 8(8):1278. https://doi.org/10.3390/math8081278

Chicago/Turabian Style

Djorić, Mirjana; Munteanu, Marian I. 2020. "Five-Dimensional Contact CR-Submanifolds in S 7 ( 1 ) " Mathematics 8, no. 8: 1278. https://doi.org/10.3390/math8081278

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