VECTOR BUNDLES ON CURVES ADMITTING A CONNECTION

Let k be any infinite perfect field. Let E be a vector bundleover a smooth projective curve defined over k. We prove thatE admits a connection if the degree of every indecomposablecomponent of E is zero. This has been proved (when k = ) inM. F. Atiyah [2] and A. Weil [7].     

ON CLIFFORD'S THEOREM FOR VECTOR BUNDLES ON ALGEBRAIC CURVES

Let X be a smooth projective curve of genus g ≥ 2 and E a rank r spanned vector bundle on X with deg(E)/rank(E) ≤ g ? 1. Here we give lower bounds for deg(E) refining the classical theorem of Clifford. Most results are for vector bundles with rank ≤ 5.     

VECTOR BUNDLES ON PROJECTIVE SPACES OVER A DISCRETE VALUATION RING

Let E be a vector bundle on P ⁿ _D, n ≥ 2, with D discrete valuation ring. Here we give a necessary and sufficient condition for the splitting of E as a direct sum of line bundles.     

BRILL－NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

Lei X be an arbitrary smooth irreducible complex projective curve, E (?) X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2,f}, where D1 , D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ H0(X, [D1] |D2) is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 2g X d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?)Im{H0(X, E) (?) H0(X,[D2]) (?) H0(X,[D2] |D2)}. From this and H0(X,E) = H0(X, [D1]) (?) Im{H0(X, E) (?) H0(X, [D2])}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.     

ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES

The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved, with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.     

THE HOMOTOPY TYPES OF THE DELETED PRODUCTS OF SOME VECTOR BUNDLES

In this paper it is shown that if W is an m-vector bundle over an n-manifold M with some conditions, then the W~k—ΔW, k-deleted product of W, and M~k ∪ΔM×S~((k-1×m+n)-1) are homotopy equivalent.     

THE FOURIER TRANSFORM FOR HOMOGENEOUS VECTOR BUNDLES OVER QUATERNION UNIT DISK

61. IntroductionLet G be a connected noncompart semisimple Lie group with finite center and K amaimal compact subgroup of G, and X = G/K the associated Riemannian symmetricspace of noncompact type.Let (Vr, f) be an irreducible unitary representation of K, and E' be the homogeneousvector bundle over G/K associated with the given representation f. It is well krmwn that across section j 6 F(E") mad be identified with a vector-vained function f: G - V. whichi. right-K-cowiaat of type TI i.…     

SUB-SIGNATURE OPERATORS, η-INVARIANTS AND A RIEMANN-ROCH THEOREM FOR FLAT VECTOR BUNDLES

The author presents an extension of the Atiyah-Patodi-Singer invariant for unitary representations [2, 3] to the non-unitary case, as well as to the case where the base manifold admits certain finer structures. In particular, when the base manifold has a fibration structure, a Riemann-Roch theorem for these invariants is established by computing the adiabatic limits of the associated η-invariants.     

丛上的相交数与Euler数

本文主要研究了带边流形上丛截面的相交数．应用作倍流形上的向量场的延拓，我们得到了带边流形上的Euler数用相交数的表示．     

EQUIVARIANT HARMONIC CYLINDERS

We prove that a primitive harmonic map is equivariant if andonly if it admits a holomorphic potential of degree one. Weinvestigate when the equivariant harmonic map is periodic and,as an application, discuss constant mean curvature cylinderswith screw motion symmetries.     

ON VECTOR VALUED ORLICZ SPACES

The theory of vector valued Orlicz spaces generated by generalized N-functions wasintroduced by M.S.Skaff(see[1,2]).But the proofs of two main theorems in [2] areincorrect.In this paper,the author exhibits an example to show the incorrectness,givesthe correct proofs and improves one of those theorems.     

CLASSIFYING INVOLUTIONS ON PR( 2k) UP TO EQUIVARIANT COBORDISM

It is proved that there are exactly k + 1 involutions on RP(2k) up to equivariant cobordism.     

RECASTING RESULTS IN EQUIVARIANT GEOMETRY

Using the language of stacks, we recast and generalize a selection of results in equivariant geometry.     

向量变分和向量拟变分不等式解的存在性定理及应用

本文利用纯量化方法及ＫＫＭ技巧,研究向量变分和向量拟变分不等式解的存在性问题,作为应用本文还研究了向量互补问题及最优化问题解的存在性及其等价性刻划。本文结果改进和推广了已有的结果。     

A NOTE ON VECTOR CASCADE ALGORITHM

AbstractThe focus of this paper is on the relationship between accuracy of multivariate refinable vector and vector cascade algorithm. We show that, if the vector cascade algorithm (1.5) with isotropic dilation converges to a vector-valued function with regularity, then the initial function must satisfy the Strang-Fix conditions.     

THE CONVEX VECTOR PROGRAMMING ON AN ORDER COMPLETE ORDERED TOPOLOGICAL VECTOR SPACE

This paper first gives several basic theorems,including some equivalent forms ofHahn-Banach Theorem on an order complete ordered vector space and an order completeordered topological vector space.Then,with these results,we can conveniently discuss theproblems of general convex vector programming.In special cases,we give thecorresponding results of Rockafellar Problem and Kuhn-Tucker's problem.     

QUOTIENTS OF CONIC BUNDLES

Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over Open image in new window by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any quotient is birationally equivalent to a quotient of other k-rational conic bundle cyclic group \( {\mathrm{\mathfrak{C}}}_{2^k} \) of order 2 ^k , dihedral group \( {\mathfrak{D}}_{2^k} \) of order 2 ^k , alternating group \( {\mathfrak{A}}_4 \) of degree 4, symmetric group \( {\mathfrak{S}}_4 \) of degree 4 or alternating group \( {\mathfrak{A}}_5 \) of degree 5 effectively acting on the base of the conic bundle. Also we construct infinitely many examples of such quotients which are not k-birationally equivalent to each other.     

ON ROTATED VECTOR FIELDS IN HIGHER-DIMENSIONAL SPACES

In this paper,the author introduces the concept of rotated vector fields in higher-dimensional spaces and proves some theorems which are similar to those in theory of rotatedvector fields in plane.Besides,some applications are given.     

VITALI-HAHN-SAKS THEOREM FOR VECTOR MEASURES ON OPERATOR ALGEBRAS

We show that the direct generalization of the Vitali–Hahn–Sakstheorem is not valid for all measures on von Neumann algebras.By applying a general equicontinuity argument, we prove a directextension of the Vitali–Hahn–Saks theorem for awide range of vector measures on von Neumann algebra s and JBWalgebras. We also characterize relatively compact sets of vectormeasures on operator algebras.