H-Semi-Invariant Submersions

Park, Kwang-Soon

doi:10.11650/twjm/1500406802

Cited by 42 publications

(28 citation statements)

References 16 publications

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“…As we know, an isometric immersion is the corresponding notion of a Riemannian submersion ( [35], [22], [21]). In the similar way, almost h-slant submanifolds, almost h-semi-invariant submanifolds, and almost h-semi-slant submanifolds correspond to almost h-slant submersions, almost h-semi-invariant submersions, and almost h-semi-slant submersions, respectively ( [38], [39], [40]). Similarly, pointwise almost h-slant submanifolds, pointwise almost h-semi-invariant submanifolds, and pointwise almost h-semi-slant submanifolds are the corresponding notions of pointwise almost h-slant submersions, pointwise almost h-semi-invariant submersions, and pointwise almost h-semi-slant submersions, respectively.…”

Section: Pointwise Almost H-semi-slant Submanifoldsmentioning

confidence: 78%

Pointwise almost h-semi-slant submanifolds

Park

2015

Int. J. Math.

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Abstract. We introduce the notions of pointwise almost h-slant submanifolds and pointwise almost h-semi-slant submanifolds as a generalization of slant submanifolds, pointwise slant submanifolds, semi-slant submanifolds, and pointwise semi-slant submanifolds. We obtain a characterization and investigate the following: the integrability of distributions, the conditions for such distributions to be totally geodesic foliations, the mean curvature vector fields on totally umbilic submanifolds, the properties of h-slant functions and h-semislant functions, the properties of non-trivial warped product proper pointwise h-semi-slant submanifolds. We also obtain the topological properties of proper pointwise almost h-slant submanifolds and give an inequality for the squared norm of the second fundamental form in terms of a warping function and a h-semi-slant function for a warped product submanifold of a hyperkähler manifold. Finally, we give some examples of such submanifolds.

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Section: Pointwise Almost H-semi-slant Submanifoldsmentioning

confidence: 78%

Pointwise almost h-semi-slant submanifolds

Park

2015

Int. J. Math.

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“…Riemannian submersions have been also considered for quaternionic Kähler manifolds [14] and para-quaternionic Kähler manifolds [4], [15]. This kind of submersions have been studied with di¤erent names by many authors (see [1], [10], [12], [21], [22], [23], [24] and more).…”

Section: Introductionmentioning

confidence: 99%

Semi-invariant semi-Riemannian submersions

Akyol¹,

Gündüzalp²

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. In this paper, we introduce semi-invariant semi-Riemannian submersions from para-Kähler manifolds onto semi-Riemannian manifolds. We give some examples, investigate the geometry of foliations that arise from the de…nition of a semi-Riemannian submersion and check the harmonicity of such submersions. We also …nd necessary and su¢ cient conditions for a semiinvariant semi-Riemannian submersion to be totally geodesic. Moreover, we obtain curvature relations between the base manifold and the total manifold.

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“…If we consider a Riemannian submersion with some additional conditions, we get many different types of submersions: An almost Hermitian submersion [33], a slant submersion [8,30], a semi-slant submersion [29], a quaternionic submersion [19], an anti-invariant quaternionic submersion and an anti-invariant octonion submersion [13], a horizontally conformal submersion [15,7], a conformal anti-invariant submersion [2], an h-conformal semi-invariant submersion and an almost h-conformal semi-invariant submersion [28]. We also refer [12,26,31,22,27].…”

Section: Introductionmentioning

confidence: 99%

Almost h-conformal slant submersions from almost quaternionic Hermitian manifolds

Park¹,

Park²

2018

Int. J. Geom. Methods Mod. Phys.

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We introduce the notions of h-conformal slant submersions and almost h-conformal slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, h-slant submersions, almost h-slant submersion and conformal slant submersions.We investigate several properties of these including the integrability of distributions, the geometry of foliations and the conditions for such maps to be totally geodesic. Further we give some examples of such maps.2000 Mathematics Subject Classification. 53C15, 53C26, 53C43.

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H-Semi-Invariant Submersions

Abstract: In this paper, we introduce the notions of the almost h-semi-invariant submersion and the h-semi-invariant submersion which may be the extended version of the notion of the semi-invariant submersion [18]. Using them, we obtain some properties. Finally, we give some examples for them.

Cited by 42 publications

References 16 publications

Pointwise almost h-semi-slant submanifolds

Pointwise almost h-semi-slant submanifolds

Semi-invariant semi-Riemannian submersions

Almost h-conformal slant submersions from almost quaternionic Hermitian manifolds

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