Abstract We study conformal $$\eta$$ ? -Einstein solitons on the framework of trans-Sasakian manifold in dimension three. Existence is discussed. Then we find some results which are where Ricci tensor cyclic parallel and Codazzi type. also consider curvature conditions with addition to manifold. use torse-for...

We show that the natural S-bundle over a projective special Kähler manifold carries the geometry of a proper affine hypersphere endowed with a Sasakian structure. The construction generalizes the geometry of the Hopf-fibration S −→ CPn in the context of projective special Kähler manifolds. As an application we have that a natural circle bundle over the Kuranishi moduli space of a Calabi-Yau thr...

We present new steady Euler solutions on the (round) 3-sphere, that bifurcate from an ansatz proposed in [11], showing these previously known are not isolated. also extend this to any Sasakian 3-manifold, such as Heisenberg group and $$SL(2, \mathbb {R})$$ .

ABS’I’RACI’. Pseudo-Sasakian manifolds M(U,E,,,g) endowed wlth a contact conformal connection are defined. It is proved tlat sucl manifolds are space forms M(K),K < O, and somo remarkable properttos of the 1,ie algebra of infinitesimal transformatton. of the principal vector feld U on M are discussed. Properties of tle leaves of a co-tsotroptc foliation on I’! and properties of the tangent bund...

In this paper, we proved that a compact Sasakian manifold [Formula: see text] with negative transverse holomorphic sectional curvature must have structure Ricci curvature. Similarly, nonpositive curvature, then the first basic Chern class is nef and Miyaoka–Yau-type inequality. When quasi-negative, obtain number

In this paper we consider contact metric R-harmonic manifolds M with ξ belonging to (κ, μ)-nullity distribution. In this context we have κ ≤ 1. If κ < 1, then M is either locally isometric to the product E × S(4), or locally isometric to E(2) (the group of the rigid motions of the Euclidean 2-space). If κ = 1, then M is an Einstein-Sasakian manifold. Mathematics Subject Classification: 53C05, 5...