We study a sequence of connections which is associated with a Riemannian metric and an almost symplectic structure on a manifold M according to a construction in [5]. We prove that if this sequence is trivial (i.e. constant) or 2-periodic, then M has a canonical Kähler structure.

A Riemannian almost paracomplex manifold is a 2n-dimensional (M,g), whose structural group O(2n,R) reduced to the form O(n,R)×O(n,R). We define scalar curvature π of this and consider relationships between s metric g its conformal transformations.

For each integer n 2 we construct a compact, geodesic, metric space X which has topological dimension n, is Ahlfors n-regular, satis es the Poincar e inequality, possesses IR as a unique tangent cone at Hn almost every point, but has no manifold points.

An existence theorem for stationary discs of strongly pseudo-convex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to certain open subsets of the tangent spaces, there exists a unique stationary disc passing through that point and tangent to the given vector. Introduction Ana...

In the present paper, we prove that if metric of a three dimensional almost Kenmotsu manifold with $\textbf{Q}\phi=\phi \textbf{Q}$ whose scalar curvature remains invariant under chracterstic vector field $\zeta$, admits non-trivial Yamabe solitons, then is constant sectional or Ricci simple.

In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of  rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces...