Let Fm = (M,F ) be a Finsler manifold and G be the Sasaki– Finsler metric on the slit tangent bundle TM0 = TM {0} of M . We express the scalar curvature ρ̃ of the Riemannian manifold (TM0, G) in terms of some geometrical objects of the Finsler manifold Fm. Then, we find necessary and sufficient conditions for ρ̃ to be a positively homogenenous function of degree zero with respect to the fiber coo...

In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann–Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI). An ...

General offset curves are treated in the context of Minkowski geometry, the geometry of the two-dimensional plane, stemming from the consideration of a strictly convex, centrally symmetric given curve as its unit circle. Minkowski geometry permits us to move beyond classical confines and provides us with a framework in which to generalize the notion of Pythagorean-hodograph curves in the case o...

One of the important tasks in optoacoustics today is development methods and tools for generating high-frequency ultrasound (above 1 MHz) liquids other media. To expand frequency range ultrasound, it was proposed to use coatings consisting focusing spheres on a fiber tip. The methodology calculating spectra depending sphere size, index refraction, parameters laser radiation developed. Two cases...

It has been recently shown that for a convex domain Ω in C and w ∈ Ω the function FΩ(w) := ( KΩ(w)λ(IΩ(w)) )1/n , where KΩ is the Bergman kernel on the diagonal and IΩ(w) the Kobayashi indicatrix, satisfies 1 ≤ FΩ ≤ 4. While the lower bound is optimal, not much more is known about the upper bound. In general it is quite difficult to compute FΩ even numerically and the highest value of it obtain...

A tangent manifold is a pair (M, J) with J a tangent structure (J2 = 0, ker J = im J) on the manifold M . A systematic study of tangent manifolds was done by I. Vaisman in [5]. One denotes by HM any complement of im J := TV . Using the projections h and v on the two terms in the decomposition TM = HM ⊕TV one naturally defines an almost complex structure F on M . Adding to the pair (M, J) a Riem...