Extensions of the mandala of Legendrian dualities for pseudo-spheres in Lorentz–Minkowski space

Izumiya, Shyūichi; Yıldırım, Handan

doi:10.1016/j.topol.2011.09.026

Cited by 12 publications

(18 citation statements)

References 14 publications

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“…and M D instead of (respectively, n T , n S , X u i and M ), we get the results given in [2,12] as special cases of some of our results in this paper.…”

Section: Spacelike Hypersurface Case In De Sitter Spacesupporting

confidence: 82%

“…Thus, the results which were given in [2], [12] and [13] are special cases of our results. On the other hand, we generalize some of the results which were obtained in [10].…”

supporting

confidence: 64%

“…Consequently, we can mention about our previous results in [2,12,13] as special cases of this paper in the following subsections.…”

Section: Spacial Casesmentioning

confidence: 82%

“…And then, in [12], they have been extended for oneparameter families depending on the parameter φ ∈ [0, π/2] of pseudo-spheres in LorentzMinkowski space as follows:…”

Section: Spacial Casesmentioning

confidence: 99%

“…As a result,taking into account these duality theorems, we have recently investigated slant geometry of spacelike hypersurfaces in the pseudo-spheres in Lorentz-Minkowski space in [2,12,13].…”

Section: Spacial Casesmentioning

confidence: 99%

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Slant geometry on spacelike submanifolds of codimension two in Lorentz–Minkowski space

Izumiya

Yıldırım

2015

Journal of Geometry and Physics

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“…and M D instead of (respectively, n T , n S , X u i and M ), we get the results given in [2,12] as special cases of some of our results in this paper.…”

Section: Spacelike Hypersurface Case In De Sitter Spacesupporting

confidence: 82%

“…Thus, the results which were given in [2], [12] and [13] are special cases of our results. On the other hand, we generalize some of the results which were obtained in [10].…”

supporting

confidence: 64%

“…Consequently, we can mention about our previous results in [2,12,13] as special cases of this paper in the following subsections.…”

Section: Spacial Casesmentioning

confidence: 82%

“…And then, in [12], they have been extended for oneparameter families depending on the parameter φ ∈ [0, π/2] of pseudo-spheres in LorentzMinkowski space as follows:…”

Section: Spacial Casesmentioning

confidence: 99%

Section: Spacial Casesmentioning

confidence: 99%

See 3 more Smart Citations

Slant geometry on spacelike submanifolds of codimension two in Lorentz–Minkowski space

Izumiya

Yıldırım

2015

Journal of Geometry and Physics

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The lightlike geometry of marginally trapped surfaces in Minkowski space-time

Honda

Izumiya

2015

J. Geom.

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The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [15] which is a natural Lorentzian analogue of the classical Euclidean differential geometry of hypersurfaces. In this paper we investigate a special class of surfaces (i.e., marginally trapped surfaces) in Minkowski space-time from the view point of the lightlike geometry.Mathematics Subject Classification (2010). 53A35, 53C50, 83C75.

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