Integral formulas are powerful tools used to obtain global results in geometry and analysis. The integral for almost multi-product manifolds, foliations multiply twisted products of Riemannian, metric-affine sub-Riemannian which this review paper is devoted, useful studying such problems as (i) the existence characterization with a given geometric property, being totally geodesic, minimal or um...

An extensive literature exists describing various techniques for the evaluation of Hankel determinants. The prevailing methods such as Dodgson condensation, continued fraction expansion, LU decomposition, all produce product formulas when they are applicable. We mention the classic case of the Hankel determinants with binomial entries 3k+2 k and those with entries 3k k ; both of these classes o...

We introduce and study a new type of soliton with potential Reeb vector field on Riemannian manifolds an almost paracontact structure corresponding to paracomplex structure. The special cases para-Einstein-like, para-Sasaki-like having torse-forming were considered. It was proved necessary sufficient condition for the manifold admit para-Ricci-like soliton, which is that para-Einstein-like. Exp...