ON THE k-REGULARITY OF SOME PROJECTIVE MANIFOLDS

Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds

In this paper we investigate the regularity of optimal transport maps for the squared distance cost on Riemannian manifolds. First of all, we provide some general necessary and sufficient conditions for a Riemannian manifold to satisfy the so-called Transport Continuity Property. Then, we show that on surfaces these conditions coincide. Finally, we give some regularity results on transport maps...

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

On the k-nullity foliations in Finsler geometry

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...

K-FLAT PROJECTIVE FUZZY QUANTALES

In this paper, we introduce the notion of {bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.

SOME PROPERTIES OF m−PROJECTIVE CURVATURE TENSOR IN KENMOTSU MANIFOLDS (COMMUNICATED BY PROFESSOR U. C. DE)

In this paper, some properties of m−projective curvature tensor in Kenmotsu manifolds are studied.