in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

in this paper, we introduce the concepts of norm and inner prod- uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.

In this article, we give a perspective on several results, old and new, concerning geometric structures of moduli spaces of Riemann surfaces with respect to the L2 metric (Weil-Petersson metric) on deformations of hyperbolic metrics. In doing so, we aim to demonstrate that the Weil-Petersson metric is suited to account for the geometry of moduli spaces while the topological type, genus in parti...

The aim of this work is to introduce and study the nondegenerate inner product $<\cdot , \cdot >_{det}$ induced by determinant map on space $Sym(2)$ symmetric $2\times 2$ real matrices. This bilinear form index $2$ defines a rational function pairs rays in plane an associated $2$-torus can be expressed with usual Hopf bundle projection $S^3\rightarrow S^2(\frac{1}{2})$. Also, trea...

0. Introduction 0.1. Quantum cohomology. Quantum cohomology of a projective algebraic manifold V is a formal deformation of its cohomology ring. Parameters of this deformation are coordinates on the space H * (V), and the structure constants are the third derivatives of a formal series Φ V (potential, or free energy) whose coefficients count the number of parametrized rational curves on V with ...

Let T (S) be the Teichmüller space of an oriented surface S of finite type. We discuss the action of subgroups of the mapping class group of S on the CAT(0)-boundary of the completion of T (S) with respect to the Weil-Petersson metric. We show that the set of invariant Borel probability measures for the Weil-Petersson flow on moduli space which are supported on a closed orbit is dense in the sp...