Quotient metrics with applications in convex geometry

Recurrent metrics in the geometry of second order differential equations

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

Geometry of splice-quotient singularities

We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate functions. The elegant way is the language of of line bundles based on Okuma’s description of the function ring of the universal abelian cover. As an easy applicat...

Submanifolds and Quotient Manifolds in Noncommutative Geometry

We define and study noncommutative generalizations of submanifolds and quotient manifolds, for the derivation-based differential calculus introduced by M. Dubois-Violette and P. Michor. We give examples to illustrate these definitions. L.P.T.H.E.-ORSAY 95/53 Laboratoire associé au Centre National de la Recherche Scientifique URA D0063

Applications of Convex and Algebraic Geometry to Graphs

RFG on Applications of Convex Geometry Lecturer : Amitabh Basu

This lecture surveys the basic definitions and important tools from lattice theory that we will need in this course. Throughout this class, we will be concerned with the n-dimensional Euclidean space Rn. For any real number r ∈ R, we denote the greatest integer smaller than or equal to r by ⌊r⌋, the smallest integer greater than or equal to r by ⌈r⌉ and {r} will be used to denote r − ⌊r⌋. Defin...