共查询到20条相似文献,搜索用时 109 毫秒
1.
Isometric immersions with parallel pluri-mean curvature (“ppmc”) in euclidean n-space generalize constant mean curvature (“cmc”) surfaces to higher dimensional Kähler submanifolds. Like cmc surfaces they allow a one-parameter family of isometric deformations rotating the second fundamental form at each point. If these deformations are trivial the ppmc immersions are called isotropic. Our main result drastically restricts the intrinsic geometry of such a submanifold: Locally, it must be a symmetric space or a Riemannian product unless the immersion is holomorphic or a superminimal surface in a sphere. We can give a precise classification if the codimension is less than 7. The main idea of the proof is to show that the tangent holonomy is restricted and to apply the Berger-Simons holonomy theorem. 相似文献
2.
We extend the ‘bundle constructions’ of calibrated submanifolds, due to Harvey–Lawson in the special Lagrangian case, and to Ionel–Karigiannis–Min-Oo in the cases of exceptional calibrations, by ‘twisting’ the bundles by a special (harmonic, holomorphic, or parallel) section of a complementary bundle. The existence of such deformations shows that the moduli space of calibrated deformations of these ‘calibrated subbundles’ includes deformations which destroy the linear structure of the fibre. 相似文献
3.
We consider the deformations of complex orbifolds with the underlying smooth structures being fixed.As a corollary,we can prove that the deformations of a Calabi-Yau orbifold is unobstructed by using standard arguments.Then we consider the period map for a family of complex Kahler orbifolds.We prove that the period map is holomorphic,horizontal and consistent with our Kodaira-Spencer map. 相似文献
4.
Robert Carlson 《Journal of Functional Analysis》1982,46(3):265-279
Isospectral deformations of differential operators with periodic coefficients are constructed by modifying a method due to Burchnall and Chaundy. If the commutant of a differential operator L of order at least two consists of polynomials in L, then L admits holomorphic families of isospectral deformations of every positive dimension. The methods are independent of the order of the operator L. 相似文献
5.
6.
Justin Sawon 《Advances in Mathematics》2008,218(3):828-864
We apply the methods of C a?ld?raru to construct a twisted Fourier-Mukai transform between a pair of holomorphic symplectic four-folds which are fibred by Lagrangian abelian surfaces. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a certain Lagrangian fibration and the derived category of twisted sheaves on its ‘mirror’ partner. As a corollary, we extend the original Fourier-Mukai transform to degenerations of abelian surfaces. Another consequence of the general theory is that the holomorphic symplectic four-fold and its mirror are connected by a one-parameter family of deformations through Lagrangian fibrations. 相似文献
7.
A harmonic function H on is said to be universal (in the sense of Birkhoff) if its set of translates is dense in the space of all harmonic functions on with the topology of local uniform convergence. The main theorem includes the result that such functions, H, can have any prescribed order and type. The growth result is compared with a similar known theorem for G.D. Birkhoff's universal holomorphic functions and contrasted with known growth theorems for MacLane-type universal harmonic and holomorphic functions. 相似文献
8.
Carsten Thomassen 《Journal of Combinatorial Theory, Series B》1983,34(3):244-257
It is proven that, if Γ0 and Γ1 are isomorphic strictly convex graphs such that their outer polygons correspond to each other and have the same orientations, then Γ0 can be continuously deformed into Γ1 such that, at each stage, the graph under consideration is convex. This extends a result of Cairns (Ann of Math.45 (2) (1944), 207–217; Amer. Math. Monthly51 (1944), 247–252) and proves a conjecture of Grünbaum and Shepard (“Proceedings, 8th British Combinatorial Conf.”, 1981). This result is applied to prove an analogous conjecture by Grünbaum and Shepard on deformations of straight graphs in general and it is shown how the proof method also can be used to verify a conjecture of Robinson (“Proceedings, 8th British Combinatorial Conf.”, 1981) on deformations of rectanguloid curves. 相似文献
9.
A. B. Mitkevich 《Mechanics of Composite Materials》2006,42(4):297-302
The deformation of pressure vessel domes in asymmetric winding with the use of two families of yarns is accompanied by shear
deformations and torsion. For the case of large deformations, a system of equations for describing the stress-strain state
of an asymmetrically reinforced netlike shell of revolution loaded with an internal pressure is obtained. It is shown that
the shear deformations depend on the deformations of both the yarn families and the deformations of meridians and parallels
of the shell. As an example, the dome of a pressure vessel in a deformed state is calculated for an initial equilibrium shape
determined on the assumption that the yarns are inextensible.
__________
Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 425–432, July–August, 2006. 相似文献
10.
Adam Harris 《Studies in Applied Mathematics》1998,101(3):309-319
The main result of this note treats the problem of unique extension of holomorphic gauge fields across closed subsets of complex Euclidean space, and is based on a corresponding extension theorem for holomorphic vector bundles due to N. P. Buchdahl and the author. Alternatively, let F be a unitary gauge field corresponding to a complex differential form of type (1, 1) (e.g., an anti self-dual Yang–Mills field on a punctured ball in C 2). As a corollary of the main theorem, it is seen that a unique extension of such F , which preserves the curvature type, is obtained if the contraction of F with a holomorphic vector field lies in the image of the ?¯-operator of the associated holomorphic vector bundle. 相似文献
11.
The deformation behavior of a 4D composite reinforced along cube diagonals under large shear deformations is examined. The investigation is based on an applied theory which allows one to perform a macromechanical analysis of composite materials with small volume contents of reinforcing yarns to an accuracy sufficient in practice. Qualitative differences between the properties of such composites under large and small shear deformations are revealed. The evolution of the structural geometry of the deformed composite material is traced. 相似文献
12.
After a finite étale cover, any Ricci-flat Kähler manifold decomposes into a product of complex tori, irreducible holomorphic symplectic manifolds, and Calabi–Yau manifolds. We present results indicating that this decomposition is an invariant of the derived category. The main idea to distinguish the derived category of an irreducible holomorphic symplectic manifold from that of a Calabi–Yau manifold is that point sheaves do not deform in certain (non-commutative) deformations of the former, whereas they do for the latter. On the way, we prove a conjecture of C?ld?raru on the module structure of the Hochschild–Kostant–Rosenberg isomorphism for manifolds with trivial canonical bundle as a direct consequence of recent work by Calaque, van den Bergh, and Ramadoss. 相似文献
13.
A. I. Shtern 《Journal of Mathematical Sciences》2004,123(4):4324-4339
We prove that irreducible unitary representations of the discrete series of simple Hermitian-symmetric Lie groups can be continuously deformed in the class of pure unitary pseudo-representations (note that these representations cannot be continuously deformed in the class of unitary representations). We also briefly recall the main definitions and facts related to the notions of quasi-symmetry and pseudo-symmetry and to the realization of representations of the holomorphic discrete series of simple hermitian-symmetric Lie groups. 相似文献
14.
The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these
spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations
of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological)
theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies
of non-commutative deformations of degree-zero line bundles. 相似文献
15.
In this paper, we consider deforming a coisotropic submanifold Y in a holomorphic Poisson manifold . Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y with an -algebra that controls the deformations of Y. This -algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y. 相似文献
16.
JianZHOU 《数学学报(英文版)》2003,19(4):695-714
We explain how deformation theories of geometric objects such as complex structures,Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson al-gebras.We use homological perturbation theory to construct A∞ algebra structures on the cohomology,and their canonically defined deformations.Such constructions are used to formulate a version of A∞ algebraic mirror symmetry. 相似文献
17.
Using the concept of inner integral curves defined by Hirschowitz we generalize a recent result by Kim, Levenberg and Yamaguchi concerning the obstruction of a pseudoconvex domain spread over a complex homogeneous manifold to be Stein. This is then applied to study the holomorphic reduction of pseudoconvex complex homogeneous manifolds X = G/H. Under the assumption that G is solvable or reductive we prove that X is the total space of a G-equivariant holomorphic fiber bundle over a Stein manifold such that all holomorphic functions on the fiber are constant. 相似文献
18.
Misha Verbitsky 《Geometric And Functional Analysis》2010,19(5):1481-1493
Let M be a compact, holomorphic symplectic Kähler manifold, and L a non-trivial line bundle admitting a metric of semipositive curvature. We show that some power of L is effective. This result is related to the hyperkähler SYZ conjecture, which states that such a manifold admits a holomorphic Lagrangian fibration, if L is not big. 相似文献
19.
D. J. Needham 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,39(3):1092-1095
We give an elementary proof that, in its domain of definition, the time-p map of a scalar, autonomous holomorphic, complex differential equation, is itself holomorphic. This result is used by Sverdlove
[1] when considering limit cycles in complex holomorphic differential equations. However no proof or reference for the result
is given in [1]. Although this result must be well established, a proof does not appear to be readily accessible in the reference
literature. 相似文献
20.
D. J. Needham 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):1092-1095
We give an elementary proof that, in its domain of definition, the time-p map of a scalar, autonomous holomorphic, complex differential equation, is itself holomorphic. This result is used by Sverdlove
[1] when considering limit cycles in complex holomorphic differential equations. However no proof or reference for the result
is given in [1]. Although this result must be well established, a proof does not appear to be readily accessible in the reference
literature. 相似文献