A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as B-metric manifold), which obtained by a contact conformal transformation of the Reeb vector field, its dual 1-form, B-metric, and associated B-metric. case in potential torse-forming field constant length vertical distribution determined studied. In this way, manifolds from one main classes studied ar...

We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a classical Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become l...

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M × Rm = TM ⊗ νM is equipped with an almost metric connection ∇̃ which almost preserves the decomposition of M × Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂ − ∇̃ with the usual derivative ∂ in Rm is almost ∇̃-parallel. Then M admits an extrinsically homogeneous immersion into Rm.

Consider a sample of n points taken i.i.d from a submanifold of Euclidean space. This defines a metric measure space. We show that there is an explicit set of scales tn → 0 such that a coarse Ricci curvature at scale tn on this metric measure space converges almost surely to the coarse Ricci curvature of the underlying manifold.

The article deals with nearly Sasakian manifolds of a constant type. It is proved that the almost Hermitian structure induced on integral maximum dimension first fundamental distribution manifold Kähler manifold. class zero type coincides manifolds. concept constancy an contact metric introduced through its Nijenhuis tensor, and criterion proved. coincidence both concepts for structure.