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51.
Let M be a real submanifold of an almost complex manifold
and let
be the maximal holomorphic subspace, for each x M. We prove that c:M,c(x)=dim
H
x
is upper-semicontinuous. 相似文献
52.
In this paper we study the holomorphic K-theory of a projective variety. This K-theory is defined in terms of the homotopy type of spaces of holomorphic maps from the variety to Grassmannians and loop groups. This theory is built out of studying algebraic bundles over a variety up to algebraic equivalence. In this paper we will give calculations of this theory for flag like varieties which include projective spaces, Grassmannians, flag manifolds, and more general homogeneous spaces, and also give a complete calculation for symmetric products of projective spaces. Using the algebraic geometric definition of the Chern character studied by the authors we will show that there is a rational isomorphism of graded rings between holomorphic K-theory and the appropriate morphic cohomology groups, in terms of algebraic co-cycles in the variety. In so doing we describe a geometric model for rational morphic cohomology groups in terms of the homotopy type of the space of algebraic maps from the variety to the symmetrized loop group U(n)/
n
where the symmetric group
n
acts on U(n) via conjugation. This is equivalent to studying algebraic maps to the quotient of the infinite Grassmannians BU(k) by a similar symmetric group action. We then use the Chern character isomorphism to prove a conjecture of Friedlander and Walker stating that if one localizes holomorphic K-theory by inverting the Bott class, then rationally this is isomorphic to topological K-theory. Finally this will allows us to produce explicit obstructions to periodicity in holomorphic K-theory, and show that these obstructions vanish for generalized flag mani-folds. 相似文献
53.
Jerry R. Muir Jr. Ted J. Suffridge 《Proceedings of the American Mathematical Society》2001,129(11):3389-3393
In this paper, we study univalent holomorphic mappings of the unit ball in that have the property that the image contains a line for some , . We show that under certain rather reasonable conditions, up to composition with a holomorphic automorphism of the ball, the mapping is an extension of the strip mapping in the plane to higher dimensions.
54.
Yu. A. Farkov 《Mathematical Notes》2000,68(2):248-254
Suppose thatB
R
d
is a ball of radiusR in ℂ
d
and σ is the standard measure on the unit sphere in ℂ
d
. ForR>1, 1≤p≤∞, and for the natural numbersl, d, byH
R
0
(l, p, d) we denote the class of functionsf holomorphic inB
R
d
and such that in the homogeneous polynomial expansion of the firstl summands the zero and radial derivatives of orderl belong to the closed unit ball of the Hardy spaceH
p
(B
R
d
). In this paper an asymptotic formula for the ε-entropy of the classH
R
0
(l, p, d) in the spacesL
p
(σ), 1≤p<∞, and
is obtained.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 286–293, August, 2000. 相似文献
55.
We study connected Lie groups whose Lie algebra is obtained as the tensor product of a real associative algebra and the algebra
of quaternions. It is proved that they carry a natural integrable
-structure. We endow such quaternionic Lie groups with a left-invariant Hermitian metric and study the identity connected component of their isometry groups. The determination of such identity connected component is illustrated with a family of examples. 相似文献
56.
Let X and Y be locally compact Hausdorff spaces and T : C0(X) C0(Y) a ring homomorphism. We completely characterize such homomorphisms and show that if T is R-linear, then T is either C-linear or C-antilinear. In any case T is continuous and there is a continuous map : Y X such that Tf = f o , f C0(X) (if T is C-linear) or
(if T is C-antilinear). Thus, extending a result of Mólnar, we also derive the general form of an isometry T.AMS Subject Classification (2000): primary 46J05, 46E25(deceased) Passed away on 24 May 1999. 相似文献
57.
Jussi Laitila 《Mathematische Nachrichten》2010,283(11):1646-1653
58.
本文推广Vogt定理到广义n-赋范空间,即证明了两个广义n-赋范空间之间的保持ρ-诱导距离映射是仿射的. 相似文献
59.
On the Isometry Groups of Hyperbolic Orbifolds 总被引:1,自引:0,他引:1
John G. Ratcliffe 《Geometriae Dedicata》1999,78(1):63-67
A generic, geometrically finite, hyperbolic n-orbifold is proved to have a finite group of isometries. 相似文献
60.
We give some multidimensional Tauberian theorems for generalized functions and show examples of their application in mathematical physics. In particular, we consider the problems of stabilizing the solutions of the Cauchy problem for the heat kernel equation, multicomponent gas diffusion, and the asymptotic Cauchy problem for a free Schrödinger equation in the norms of different Banach spaces among others. 相似文献