Trajectories on real hypersurfaces of type (B) in a complex hyperbolic space are not of order 2

Bao, Tuya; Adachi, Toshiaki

doi:10.1016/j.difgeo.2012.05.005

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…We can apply now [25,Theorem 4] to see thatγ belongs to a totally geodesic complex submanifold of B 2n of complex dimension 1. Hence,γ lies in a certain hyperbolic plane CH 1 (k) ≡ H 2 (k) of constant negative curvature k. See also [3,7,8].…”

Section: Magnetic Curves In B 2n × Rmentioning

confidence: 96%

“…Adachi and Bao [6] showed that the fundamental 2-form of an orientable real hypersurface in a Kähler manifold is closed. They called a magnetic field on real hypersurfaces given by constant multiple of the fundamental 2-form a Sasakian magnetic field and they studied the magnetic trajectories on real hypersurfaces of type A in CM n (c) in [6], and of type B in the hyperbolic complex space CH n (c) in [7,8].…”

Section: Magnetic Curves In B 2n × Rmentioning

confidence: 99%

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Magnetic curves in Sasakian manifolds

Druţă-Romaniuc¹,

Inoguchi²,

Munteanu³

et al. 2021

JNMP

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In this paper we classify the magnetic trajectories corresponding to contact magnetic fields in Sasakian manifolds of arbitrary dimension. Moreover, when the ambient is a Sasakian space form, we prove that the codimension of the curve may be reduced to 2. This means that the magnetic curve lies on a 3-dimensional Sasakian space form, embedded as a totally geodesic submanifold of the Sasakian space form of dimension (2n + 1).

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Section: Magnetic Curves In B 2n × Rmentioning

confidence: 96%

Section: Magnetic Curves In B 2n × Rmentioning

confidence: 99%

Magnetic curves in Sasakian manifolds

Druţă-Romaniuc¹,

Inoguchi²,

Munteanu³

et al. 2021

JNMP

View full text Add to dashboard Cite

show abstract

“…In their papers [3] and [4] they estimated the length of circular trajectories on real hypersurface of type (A 1 ) in a complex projective space and in a complex hyperbolic space. They studied the trajectories under Sasakian magnetic field on real hypersurfaces of type (B) in a complex hyperbolic space in [5] and [6]. Except the above real hypersurfaces of types (A) and (B) there are real hypersurface of types (C),(D) and (E) in a complex projective space, which are called real hypersurfaces of exceptional type.…”

Section: Introductionmentioning

confidence: 99%