TAILIEUCHUNG - Conformal anti-invariant submersions from almost Hermitian manifolds

We introduce conformal anti-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arose from the definition of a conformal submersion, and find necessary and sufficient conditions for a conformal anti-invariant submersion to be totally geodesic. | Turk J Math (2016) 40: 43 – 70 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Conformal anti-invariant submersions from almost Hermitian manifolds ˙ 2,∗ Mehmet Akif AKYOL1 , Bayram S ¸ AHIN Department of Mathematics, Faculty of Science and Arts, Bing¨ ol University, Bing¨ ol, Turkey 2 ˙ on¨ Department of Mathematics, Faculty of Science and Arts, In¨ u University, Malatya, Turkey 1 Received: • Accepted/Published Online: • Final Version: Abstract: We introduce conformal anti-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arose from the definition of a conformal submersion, and find necessary and sufficient conditions for a conformal anti-invariant submersion to be totally geodesic. We also check the harmonicity of such submersions and show that the total space has certain product structures. Moreover, we obtain curvature relations between the base space and the total space, and find geometric implications of these relations. Key words: Riemannian submersion, anti-invariant submersion, conformal submersion, conformal anti-invariant submersion 1. Introduction One of the main methods to compare two manifolds and transfer certain structures from a manifold to another manifold is to define appropriate smooth maps between them. Given two manifolds, if the rank of a differential map is equal to the dimension of the source manifold, then such maps are called immersions and if the rank of a differential map is equal to the target manifold, then such maps are called submersions. Moreover, if these maps are isometric between manifolds, then the immersion is called isometric immersion (Riemannian submanifold) and the submersion is called Riemannian submersion. Riemannian submersions between Riemannian manifolds were studied by O’Neill [18] and Gray [10]; for recent .

• Toán học
• Riemannian submersion
• Anti invariant submersion
• Conformal submersion
• Conformal anti invariant submersion
• Totally geodesic
• Warped product
• Kenmotsu manifold
• Anti invariant
• Riemannian map
• Kaehlerian manifold
• Conformal holomorphic Riemannian map
• Conformal antiinvariant Riemannian map
• Almost paracontact metric manifold
• Semi Riemannian submersion
• Paracontact semi Riemannian submersion
• Paracontact structure
• Total manifold
• Almost contact metric manifold
• Cosymplectic manifold
• Pointwise slant submersion
• Riemannian manifolds
• Semi slant submanifolds
• Semi slant
• Totally umbilical
• Kaehler manifold
• Semiparallel submanifold
• Generalized Sasakian space form
• Laplacian of the second fundamental form
• Totally geodesic submanifold
• Certain conditions
• Riemannian warped product manifold
• Vertical and horizontal distributions
• Pseudo umbilical submanifold
• Curvature invariant submanifold