Finding the fastest path to a desired destination is vitally important task for microorganisms moving in fluid flow. We study this problem by building an analytical formalism overdamped microswimmers on curved manifolds and arbitrary flows. show that solution corresponds geodesics of Randers metric, which asymmetric Finsler metric reflects irreversible character problem. Using example spherical...

The aim of this paper is twofold. Firstly, we will investigate the link between condition for functions $\phi(s)$ from $(\alpha, \beta)$-metrics Douglas type to be self-concordant and k-self concordant, other objective continue recently new introduced \beta)$-metric ([17]): $$ F(\alpha,\beta)=\frac{\beta^{2}}{\alpha}+\beta+a \alpha where $\alpha=\sqrt{a_{ij}y^{i}y^{j}}$ a Riemannian metric; $\b...

We study the distribution of type IIB flux vacua in the moduli space near various singular loci, e.g. conifolds, ADE singularities on P, Argyres-Douglas point etc, using the AshokDouglas density det(R+ω). We find that the vacuum density is integrable around each of them, irrespective of the type of the singularities. We study in detail an explicit example of an Argyres-Douglas point embedded in...

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

‎based on a definition for circle in finsler space‎, ‎recently proposed by one of the present authors and z‎. ‎shen‎, ‎a natural definition of extrinsic sphere in finsler geometry is given and it is shown that a connected submanifold of a finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...