We prove that if $$\tau $$ is a large positive number, then the atomic Goldberg-type space $${\mathfrak {h}}^1(N)$$ and {h}}_{{\mathscr {R}}_\tau }^1(N)$$ of all integrable functions on N which local Riesz transform $${\mathscr integrable, are same any complete noncompact Riemannian manifold with Ricci curvature bounded from below injectivity radius. also relate to harmonic slice $$N\times (0,\...

the geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on tm. the metrizability of a given semispray is of special importance. in this paper, the metric associated with the semispray s is applied in order to study some types of foliations on the tangent bundle which are compatible with sode structure. indeed, suff...

It is shown that every bundle ! M of complex spinor modules over the Cliiord bundle Cl(g) of a Riemannian space (M; g) with local model (V; h) is associated with an lpin (\Lipschitz") structure on M, this being a reduction of the O(h)-bundle of all orthonormal frames on M to the Lips-chitz group Lpin(h) of all automorphisms of a suitably deened spin space. An explicit construction is given of t...

We estimate the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang for the first Dirichlet eigenvalue.

We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schrödinger operator with magnetic wells on a noncompact Riemannian manifold M such that H(M, R) = 0 equipped with a properly disconnected, cocompact action of a finitely generated, discrete group of isometries has an arbitrarily large number of spectral gaps in the semi-classical limit.

Let h ∼ i be arbitrary. It is well known that k ≡ ∅. We show that there exists a Riemannian, finite, everywhere regular and continuous pseudo-Cauchy, canonically linear matrix. Recently, there has been much interest in the extension of subrings. Therefore here, splitting is trivially a concern.

B.Y. Chen [5] established a sharp inequality for the warping function of a warped product submanifold in a Riemannian space form in terms of the squared mean curvature. Later, in [4], he studied warped product submanifolds in complex hyperbolic spaces. In the present paper, we establish an inequality between the warping function f (intrinsic structure) and the squared mean curvature ‖H‖2 and th...