A Koszul–Vinberg manifold is a M endowed with pair $$(\nabla ,h)$$ where $$\nabla $$ flat connection and h symmetric bivector field satisfying generalized Codazzi equation. The geometry of such manifolds could be seen as type bridge between Poisson pseudo-Riemannian geometry, has been highlighted in our previous article [Contravariant Pseudo-Hessian their associated structures. Differential Geo...

If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of  graph(f) is as big as possible and the lower box dimension of graph(f) is as small as possible.  

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...

Recently manifold structures have attracted attentions in two folds in the machine learning literature. One is in the manifold learning problem, that is learning the intrinsic manifold structure in high dimensional datasets. Another is in the information geometric approach to learning – exploiting the geometry of the parameter space of learning machines such as neural networks for improving con...

We answer in the affirmative question posed by Conti and Rossi [7,8] on existence of nilpotent Lie algebras dimension 7 with an Einstein pseudo-metric nonzero scalar curvature. Indeed, we construct a left-invariant pseudo-Riemannian metric $g$ signature $(3, 4)$ group 7, such that is not Ricci-flat. show cannot be induced any closed $G_2^*$-structure group. Moreover, some results harmonic $G_2^...

The study of weakly symmetric and weakly projective symmetric manifold were initiated by Tamassy and Binh in 1989. Later on several authors studied weakly symmetric Riemannian manifold and analogous structures, viz. Weakly Ricci symmetric, weakly projective symmetric and weakly conformally symmetric Riemannian manifolds. At first we cited examples of weakly symmetric Riemannian manifolds. Next ...

We give a condition on Riemannian submersions from a Riemannian manifold M to a Riemannian manifold N which will ensure that it induces a differential operator on N from the Laplace-Beltrami operator on M . Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion. 2000 Mathematics Subject Classification. Primary 58J65, 53C21.

The aim of the present paper is to improve an existing blind image deblurring algorithm, based on independent component learning paradigm, by manifold calculus. original technique analysis algorithm applied a set pseudo-images obtained Gabor-filtering blurred and adapt-and-project paradigm. A comparison between improved method shows that unit hypersphere Riemannian-gradient outperforms strategy...

Given the class of Finsler spaces with Lorentzian signature [Formula: see text] on a manifold endowed timelike vector field satisfying at any point slit tangent bundle, pseudo-Riemannian metric defined is associated to fundamental tensor text]. Furthermore, an affine, torsion free connection Chern determined by The definition average does not make use Therefore, there no direct relation between...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...