Riemannian submersions From Almost Hermitian Manifolds
Küçük Resim Yok
Tarih
2017
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Academic Press Ltd-Elsevier Science Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this chapter, we introduce various new Riemannian submersions from almost Hermitian manifolds on to Riemannian manifolds. In section 1, we first review almost Hermitian manifolds and their submanifolds, and give brief information about holomorphic submersions and invariant Riemannian submersions. In this section, we also present three important maps, namely almost complex or holomorphic maps, pseudo-horizontally weakly conformal maps, and pluriharmonic maps, defined between almost complex manifolds and Riemannian manifolds. Then, in section 2, we introduce anti-invariant Riemannian submersions from almost Hermitian manifolds to Riemannian manifolds, and show that such submersions are useful to investigate the geometry of total space. In sections 3 and 4, as a generalization of anti-invariant submersions and invariant submersions, we also introduce semi-invariant submersions and slant submersions. In section 5, as a generalization of slant submersions we consider point-wise slant submersions and show that such submersions have rich geometric properties. In section 6, we define and study generic submersions as a generalization of semi-invariant submersions. In sections 7 and 8, we introduce semi-slant submersions and hemi-slant submersions as generalizations of semi-invariant submersions and slant submersions. In section 9, we check the Einstein conditions of the base space for anti-invariant submersions. In the last section, we investigate various submersions in this chapter in terms of Clairaut's relation.
Açıklama
Anahtar Kelimeler
almost Hermitian manifold, Kahler manifold, complex space form, almost complex map, holomorphic map, pseudo-horizontally weakly conformal map, Pluriharmonic map, CR-submanifold, slant submanifold, generic submanifold, semi-slant submanifold, hemi-slant submanifold, point-wise slant submanifold, skew CR-submanifold, holomorphic submersion, invariant submersion, anti-invariant submersion, Lagrangian submersion, tangent bundle, Sasaki metric, semi-invariant submersion, pointwise slant submersion, generic submersion, semi-slant submersion, hemi-slant submersion, Einstein manifold, Clairaut submersion
Kaynak
Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications
WoS Q Değeri
N/A
