Results 1 to 10 of about 1,053 (160)

CR submanifolds of the six-sphere

, 2010
Let M be a Riemannian submanifold of the six dimensional sphere equipped with its almost complex structure J. It is natural to investigate submanifolds M according to their relations to J. If the tangent bundle of M is invariant for J, then M is an almost complex submanifold, and if J maps the tangent bundle into the corresponding normal bundle M is a ...
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Submersions of CR submanifolds

Submersions of CR submanifolds
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Submersions of CR Submanifolds

2016
O’Neill introduced the notion of Riemannian submersions (cf. O’Neill, Mich. Math. J. 13, 459–469, 1966, [28]). For the submersion \(\pi :M\longrightarrow N\) of a CR submanifold M of a Kaehler manifold \(\bar{M}\) onto an almost Hermitian manifold N, Kobayashi (cf. Kobayashi, Tohoku Math. J.
Mohammad Hasan Shahid, Falleh R. Al-Solamy, Mohammed Jamali   +2 more
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On CR-submanifolds of Hermitian manifolds

Israel Journal of Mathematics, 1979
In this paper we consider a CR-submanifold of a Hermitian manifold and prove various integrability theorems on the submanifold. When the ambient space is Kaehlerian a number of differential geometric results are also obtained.
Blair, David E., Chen, Bang-Yen
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Paraquaternionic CR-Submanifolds

2016
Paraquaternionic structures, at first known as quaternionic structures of second kind, are due to P. Libermann. Their study parallels that of quaternionic manifolds, yet relies on the algebra of paraquaternionic numbers. The counterpart in odd dimension of a paraquaternionic structure was introduced in 2006 by S. Ianus, R. Mazzocco and G.E.
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Ideal CR Submanifolds

2016
This chapter surveys some of the known results on \(\delta \)-ideal CR submanifolds in complex space forms, the nearly Kahler 6-sphere and odd dimensional unit spheres. In addition, the relationship between \(\delta \)-ideal CR submanifolds and critical points of the \(\lambda \)-bienergy functional is mentioned.
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Lorentzian geometry of CR submanifolds

Acta Applicandae Mathematicae, 1989
A. Bejancu defined CR submanifolds of differentiable manifolds with a (positive definite) Riemannian metric and almost Hermitian structure as a generalization of holomorphic submanifolds and totally real submanifolds. In this article, the notion of CR submanifold is extended to orientable Lorentz submanifolds of semi-Riemannian manifolds with an almost
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CR-Submanifolds of the Nearly Kähler 6-Sphere

2016
There is an almost complex structure J on the sphere S6(1) defined by multiplication of the Cayley numbers. This structure is nearly Kähler. A submanifold of a manifold with an almost complex structure is CR, by Bejancu, if it has a differentiable holomorphic distribution H such that its orthogonal complement H⊥⊂TM is a totally real distribution.
Antić, Miroslava, Vrancken, Luc
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Lorentzian Geometry and CR-Submanifolds

2016
This paper contains an up-to-date information on the Lorentzian geometry of CR-submanifolds, contact CR-submanifolds and globally framed CR-submanifolds (M, g) of an indefinite semi-Riemannian manifold. In view of the large number of excellent paper appearing in this field, we focus on those key results whose Lorentzian geometry is different than their
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