The present paper deals with metallic K?hler manifolds. Firstly, we define a tensor H which can be written in terms of the (0,4)-Riemannian curvature and fundamental 2-form manifold study its properties some hybrid tensors. Secondly, weobtain conditions under Hermitian is conformal to manifold. Thirdly, prove that recurrency implies also obtain Riemannian form conformally recurrent non-zero sca...

Multiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles. Given a compact Riemannian manifold (X, g), its real homology H∗(X, R) is naturally endowed with the stable norm. Briefly, if h ∈ Hk(X, R) then the stable norm of h is the infimum of the Riemannian kvolumes of real cycles representing h. The stable k-systole is the minimum of the stable no...

‎The notion of quasi-Einstein metric in physics is equivalent to the notion of Ricci soliton in Riemannian spaces‎. ‎Quasi-Einstein metrics serve also as solution to the Ricci flow equation‎. ‎Here‎, ‎the Riemannian metric is replaced by a Hessian matrix derived from a Finsler structure and a quasi-Einstein Finsler metric is defined‎. ‎In compact case‎, ‎it is proved that the quasi-Einstein met...

We prove that the weak Riemannian metric induced by the fractional Sobolev norm H on the diffeomorphisms group of the circle is geodesically complete, provided s > 3/2.

The paper generalizes and extends the notions of dual connections statistical manifold, with without torsion. Links deformation algebras Riemannian Rinehart are established. semi-Riemannian manifolds admitting flat torsion characterized, thus solving a problem suggested in 2000 by S. Amari H. Nagaoka. New examples constructed, within beyond classical setting. invariant structures on Lie groups ...

We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R into a pseudoRiemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point is actually smooth harmonic everywhere. Introduction Given n ∈ N and two nonnegat...