On quasi bi-slant submersions from Sasakian manifolds onto Riemannian manifolds
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On quasi bi-slant submersions from Sasakian manifolds onto Riemannian manifolds Rajendra Prasad1 · Punit Kumar Singh1
· Sushil Kumar2
Received: 22 September 2019 / Accepted: 2 September 2020 © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2020
Abstract In this paper, we study the quasi bi-slant submersions from Sasakian manifolds onto Riemannian manifolds. We define quasi bi-slant submersions from almost contact metric manifolds onto Riemannian manifolds which are generalization of hemi-slant submersions and semislant submersions with some examples. We also discuss the geometry of leaves of distributions which are involved in the definition of this submersion and obtain coditions for such submersions to be integrable and totally geodesic. Further, we give a characterization theorem for proper quasi bi-slant submersions with totally umbilical fibres. Keywords Riemannian submersions · Semi-invariant submersions · Quasi bi-slant submersions Mathematics Subject Classification 00A11 · 53C15 · 53C43 · 53B20 · 55B55
1 Introduction Riemannian submersions are very important and interesting topic of differential geometry. Riemannian submersions are related to physics and mathematics both and have their important applications in Yang–Mills theory [4], Kaluza–Klein theory [5,12] supergravity and superstring theories [13]. Firstly, in 1966, O’ Neill [16] initiated the theory of Riemannian submersion and Gray [9] extended this theory in 1967. Watson [26] introduced almost complex type of Riemannian submersions in 1976. He also defined and studied almost Hermitian submersions between almost Hermitian manifolds. In 1985, Chinea [6] extended the theory of Hermitian submer-
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Punit Kumar Singh [email protected] Rajendra Prasad [email protected] Sushil Kumar [email protected]
1
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India
2
Department of Mathematics, Shri Jai Narain Post Graduate College, Lucknow, India
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R. Prasad et al.
sion and intoduced the notion of almost Hermitian submersion which has been extended to different kinds of sub-classes of almost contact manifolds. Several good results related to Riemannian and almost Hermitian submersion can be found in [8,10]. In 2013, Sahin [17] introduced the semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds which was a generalization of holomorphic submersions and anti-invariant submersions [21]. Further, Sahin [18] introduced the notion of slant submersions from almost Hermitian manifolds onto arbitrary Riemannian manifolds. Several geometers studied different kinds of Riemannian submersions between Riemannian manifolds [1,11,19,20,22–24] etc. In 2013, Park and Prasad [14] introduced semi-slant submersions from an almost Hermitian manifold onto a Riemannian manifold. Later, In 2015, Sahin introduced hemi-slant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds and also gave decomposition theorem for such submersio
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