Connections on Complex Finsler Manifold

We introduce Finsler metric on complex manifold and discuss connections induced by this metric.     

Laplacian on Complex Finsler Manifolds

In this paper, the Laplacian on the holomorphic tangent bundle T1,0M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M,F). Utilizing the initiated “Bochner technique”, a vanishing theorem for vector fields on the holomorphic tangent bundle T1,0M is obtained.     

Finsler spaces with recurrent pseudocurvature tensor

Sinha [2] has defined pseudocurvature tensor field in ann-dimensional Finsler spaceF _n. In the present paper we have studied some recurrent properties of pseudocurvature tensor.     

复Finsler流形上的Hodge-Laplace算子

本文定义了强拟凸复Finsler流形上的Hodge-Laplace算子,并给出其水平部分的局部坐标表示．     

关于复Finsler流形的一个注记

设(M,G)为n维复Finsler流形,TM为M的全纯切丛,得到了TM上的Hermite度量hTM=G(-ij)(z,v)dzi(×)d(-z)j+G(-ij)(z,v)δvi(×)δ(-v)j为K(a)hler度量的充要条件是M为全纯曲率为0的Kahler流形,其中G(-ij)=(а)2G/(а)vi(а)(-v)j,1≤i,j≤n.推广了Cao-Wong的某些结果.     

复Finsler流形上的Koppelman-Leray-Norguet公式

利用不变积分核(Berndtsson核),复Finsler度量和联系于Chern-Finsler联络的非线性联络,研究复Finsler流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的积分表示,得到了(p,q)型微分形式的Koppelman-Leray-Norguet公式和■-方程的解．作为应用,利用复Finsler度量和联系于Chern-Finsler联络的非线性联络,给出了Stein流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的Koppelman- Leray-Norguet公式以及■-方程的解,并且得到了Stein流形上实非退化强拟凸多面体上(p,q)型微分形式的积分表示式和■-方程的解．     

RETRACTED: Complex Bogoslovsky Finsler metrics

The Cauchy problem of the Landau equation with potential forces on torus is investigated. The global existence of solutions with the symmetry of origin and the exponential convergence rate in time to the steady state are obtained for any initially smooth, periodic, origin symmetric small perturbation.     

Grothendieck operators on tensor products

We prove that for Banach spaces and operators , the tensor product is a Grothendieck operator, provided is a Grothendieck operator and is compact.

     

Simple tensor products

Let ℱ be the category of finite-dimensional representations of an arbitrary quantum affine algebra. We prove that a tensor product S ₁ ⊗⋅⋅⋅⊗ S _N of simple objects of ℱ is simple if and only S _i ⊗ S _j is simple for any i<j.     

Graded tensor products

We study the polynomial identities of regular algebras, introduced in [A. Regev, T. Seeman, Z₂-graded tensor products of P.I. algebras, J. Algebra 291 (2005) 274-296]. For example, a finite-dimensional algebra is regular if it has a basis whose multiplication table satisfies some commutation relations. The matrix algebra M_n(F) over the field F is regular, which is closely related to M_n(F) being Z_n-graded. We study the polynomial identities of various types of tensor products of such algebras. In particular, using the theory of Hopf algebras, we prove a far reaching extension of the A⊗B theorem for Z₂-graded PI algebras.     

Dunford-Pettis like properties on tensor products

In this paper we study equivalent formulations of the DP^? P_p (1 < p < ∞). We show that X has the DP^? P_p if and only if every weakly-p-Cauchy sequence in X is a limited subset of X. We give su?cient conditions on Banach spaces X and Y so that the projective tensor product X ?_π Y, the dual (X ?_? Y)^? of their injective tensor product, and the bidual (X ?_π Y)^?? of their projective tensor product, do not have the DP P_p, 1 < p < ∞. We also show that in some cases, the projective and the injective tensor products of two spaces do not have the DP^? P_p, 1 < p < ∞.     

Biderivations on tensor products of algebras

Let A be a noncommutative unital prime algebra and let S be a commutative unital algebra over a field 𝔽. We describe the form of biderivations of the algebra A?S. As an application, we determine the form of commuting linear maps of A?S.     

共形复Finsler流形上的交换公式

设M为n维复流形,M^-～=T~（1,0）M-{0},F为M上的强拟凸复Finsler度量, F^-=e^σF为F的共形变换。本文得到定义在M^-上的各种Hermitian张量场分别关于复Finsler流形（M,F）和（M,F^-）的复Rund联络求共变微分的各种交换公式。