The dualistic structure of statistical manifolds in information geometry yields eight types (possibly mixed type) geodesic triangles passing through three given points, the triangle vertices. interior angles can sum up to $$\pi $$ like Euclidean/Mahalanobis flat geometry, or exhibit otherwise angle excesses defects. In this work, we initiate study dually spaces, termed Bregman manifolds, where ...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

The object of this offering article is to introduce the notion *- Miao-Tam critical equation on almost contact metric manifolds and it studied Kenmotsu with some nullity condition. It proved that if a (2n + 1)-dimensional (k, µ)!-almost manifold (M, g) satisfies *-Miao-Tam equation, then *-Ricci flat locally isometric product space. Finally, result verified by an example.

The well-known Funk metric F (x, y) is projectively flat with constant flag curvature K = −1/4 and the Hilbert metric Fh(x, y) := (F (x, y) + F (x,−y))/2 is projectively flat with constant curvature K = −1. These metrics are the special solutions to Hilbert’s Fourth Problem. In this paper, we construct a non-trivial R-flat spray using the Funk metric. It is then an inverse problem in the calcul...

In this thesis we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be spectrally rigid over a stratum with enough complexity, extending a result of Duchin-LeiningerRafi. Specifically, for any stratum with more unmarked zeroes than the ...

In this article we continue studying the Ricci-flat Riemannian metrics that were constructed in [1]. On closer examination it turned out that they possess a number of remarkable properties; in particular, they have the holonomy group SU(2), so presenting special Kähler metrics. The metrics of holonomy SU(2) are interesting because of their applications in mathematical physics. In superstring th...