This paper studies conformal and related changes of the product metric on the product of two almost contact metric manifolds. It is shown that if one factor is Sasakian, the other is not, but that locally the second factor is of the type studied by Kenmotsu. The results are more general and given in terms of trans-Sasakian, α-Sasakian and β-Kenmotsu structures.
It is proved that the normal bundle of a distribution on a riemannian manifold admits a conformal curvature if and only if is a conformal foliation. Then is conformally flat if and only if vanishes. Also, the Pontrjagin classes of can be expressed in terms of .
In this paper we investigate one-dimensional sectional curvatures of Riemannian manifolds, conformal deformations of the Riemannian metrics and the structure of locally conformally homogeneous Riemannian manifolds. We prove that the nonnegativity of the one-dimensional sectional curvature of a homogeneous Riemannian space attracts nonnegativity of the Ricci curvature and we show that the inverse is incorrect with the help of the theorems O. Kowalski-S. Nikčevi'c [K-N], D. Alekseevsky-B. Kimelfeld...
It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying 0 < Ric ≤ (n-1)(2-nc/λ₁)c for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold forces it to...
For odd-dimensional Poincaré–Einstein manifolds , we study the set of harmonic -forms (for ) which are (with ) on the conformal compactification of . This set is infinite-dimensional for small but it becomes finite-dimensional if is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology and the kernel of the Branson–Gover [3] differential operators on the conformal infinity . We also relate the set of forms in the kernel of to the conformal...
By introducing the ℱ-stress energy tensor of maps from an n-dimensional Finsler manifold to a Finsler manifold and assuming that (n-2)ℱ(t)'- 2tℱ(t)'' ≠ 0 for any t ∈ [0,∞), we prove that any conformal strongly ℱ-harmonic map must be homothetic. This assertion generalizes the results by He and Shen for harmonics map and by Ara for the Riemannian case.