We revisit construction of the Atiyah-Hitchin manifold in generalized Legendre transform approach. This is originally studied by Ivanov and Rocek subsequently investigated more Ionas, latter which explicit forms K\"ahler potential metric are calculated. There a difference between former latter. In approach, constructed from contour integration one function with holomorphic coordinates. The choi...

We find the necessary and sufficient conditions for a sequential warped product manifold to be quasi-Einstein manifold. also investigate standard static space-time generalized Robertson-Walker of quasi-constant curvature.

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze d...

We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over saturated chains in the Bruhat order. We derive several explicit formulas for these polynomials, and investigate their relations with Schubert polynomials, harmonic polynomials, Demazure characters, and generalized Litt...

We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over saturated chains in the Bruhat order. We derive several explicit formulas for these polynomials, and investigate their relations with Schubert polynomials, harmonic polynomials, Demazure characters, and generalized Litt...