Degrees of Maps between Grassmann Manifolds

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Reciprocal Degree Distance of Grassmann Graphs

Recently, Hua et al. defined a new topological index based on degrees and inverse of distances between all pairs of vertices. They named this new graph invariant as reciprocal degree distance as 1 { , } ( ) ( ( ) ( ))[ ( , )] RDD(G) = u v V G d u  d v d u v , where the d(u,v) denotes the distance between vertices u and v. In this paper, we compute this topological index for Grassmann graphs.

Pluriharmonic Tori, Configurations of Points on Rational or Elliptic Curves and Another Type of Spectral Data

This paper is made up of five sections. The first four sections are expositary notes of [9] and [10]. In the last section, we introduce another type of spectral data. Recently, McIntosh [5] proved that some class of pluriharmonic maps from complex vector spaces into complex Grassmann manifolds or projective unitary groups correspond to maps constructed from triplets (X,π,L), consisting of auxil...

Introduction to Grassmann Manifolds and Quantum Computation

The aim of this paper is to give a hint for thinking to graduate or undergraduate students in Mathematical Physics who are interested in both Geometry and Quantum Computation. First I make a brief review of some properties on Grassmann manifolds and next I show a path between Grassmann manifolds and Quantum Computation which is related to the efficiency of quantum computing. ∗E-mail address : f...

The Geometry and Topology on Grassmann Manifolds

This paper shows that the Grassmann Manifolds GF(n,N) can all be imbedded in an Euclidean space MF(N) naturally and the imbedding can be realized by the eigenfunctions of Laplacian △ on GF(n,N). They are all minimal submanifolds in some spheres of MF(N) respectively. Using these imbeddings, we construct some degenerate Morse functions on Grassmann Manifolds, show that the homology of the comple...