We introduce anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds onto semi-Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a semi-Riemannian submersion, and check the harmonicity of such submersions. We also obtain curvature relations between the base manifold and the total manifold.
Abstract. In this paper, we introduce semi-slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give some examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a semi-slant submersion to be totally geodesic.
IntroductionGiven a C 8 -submersion π from a Riemannian manifold pM, gq onto a Riemannian manifold pB, g 1 q, there are several kinds of submersions according to the conditions on it: e.g. Riemannian submersion ([5] [15], the author studied the slant and semi-slant submanifolds of an almost product Riemannian manifold. Let pM, g, F q be an almost product Riemannian manifold. A Riemannian submersion π : pM, g, F q Ñ pN, g 1 q is called a slant submersion if the angle θpXq between F X and the space kerpπ˚q p is constant for any nonzero X P T p M and p P M [6]. We call θpXq a slant angle. The paper is organized as follows. In Section 2 we recall some notions needed for this paper. In Section 3 we give definition of semi-slant submersions and provide examples. We also investigate the geometry of leaves of the distributions. Finally, we give necessary and sufficient conditions for such submersions to be totally geodesic.2010 Mathematics Subject Classification: 53C15, 53B20, 53C43.
Akyol [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistics 2017; 462: 177-192] defined and studied conformal antiinvariant submersions from cosymplectic manifolds.The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field ξ is a vertical vector field) from cosymplectic manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, and conformal antiinvariant submersions. More precisely, we mention many examples and obtain the geometries of the leaves of vertical distribution and horizontal distribution, including the integrability of the distributions, the geometry of foliations, some conditions related to total geodesicness, and harmonicity of the submersions. Finally, we consider a decomposition theorem on the total space of the new submersion.
In this paper, we investigate some geometric properties of three types of slant submersions whose total space is an almost paracontact metric manifold.
Mathematics Subject Classification (2010). 53C15,53C40
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.