On the Degeneration of Harmonic Sequences from Surfaces into Complex Grassmann Manifolds

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...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Quantum Cohomology Rings of Fano Manifolds and a Formula of Vafa and Intriligator

Quantum multiplications on the cohomology of symplectic manifolds were first proposed by the physicist Vafa [Va2] based on Witten’s topological sigma models [Wi1]. In [RuTi], Ruan and the second named author gave a mathematical construction of quantum multiplications on cohomology groups of positive symplectic manifolds (cf. Chapter 1). The construction uses the Gromov-Ruan-Witten invariants (G...

GEOMETRIZATION OF HEAT FLOW ON VOLUMETRICALLY ISOTHERMAL MANIFOLDS VIA THE RICCI FLOW

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

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...