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81.
An integral formula is derived, relating the six irreducible components of the intrinsic torsion of an SpnSp1 structure on a compact 4n-dimensional manifold with the Riemann curvature tensor. Some consequences of the formula are studied. 相似文献
82.
Peter M. Gruber 《Monatshefte für Mathematik》2002,135(4):279-304
We estimate the error of asymptotic formulae for volume approximation of sufficiently differentiable convex bodies by circumscribed
convex polytopes as the number of facets tends to infinity. Similar estimates hold for approximation with inscribed and general
polytopes and for vertices instead of facets. Our result is then applied to estimate the minimum isoperimetric quotient of
convex polytopes as the number of facets tends to infinity.
Received 16 July 2001 相似文献
83.
Julien Roth 《Differential Geometry and its Applications》2007,25(5):485-499
We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. In the hyperbolic space, we show that if the volume of M is 1, then there exists a constant C depending on the dimension of M and the L∞-norm of the second fundamental form B such that the pinching condition (where H is the mean curvature) implies that M is diffeomorphic to an n-dimensional sphere. We prove the corresponding result for hypersurfaces of the Euclidean space and the sphere with the Lp-norm of H, p?2, instead of the L∞-norm. 相似文献
84.
Mohammed Larbi Labbi 《Mathematische Nachrichten》2015,288(4):402-411
The Weitzenböck curvature operators are the curvature terms of order zero that appear in the well‐known classical Weitzenböck formula. In this paper, we use the formalism of double forms to prove a simple formula for these operators and to study their geometric properties. 相似文献
85.
This paper analyzes the relation between the local rank-structure of a regular analytic matrix function and the one of its inverse function. The local rank factorization (lrf) of a matrix function is introduced, which characterizes extended canonical systems of root functions and the local Smith form. An interpretation of the local rank factorization in terms of Jordan chains and Jordan pairs is provided. Duality results are shown to hold between the subspaces associated with the lrf of the matrix function and the one of its reduced adjoint. 相似文献
86.
Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A:V→V and A∗:V→V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A∗Vi⊆Vi-1+Vi+Vi+1 for 0?i?d, where V-1=0 and Vd+1=0; (iii) there exists an ordering of the eigenspaces of A∗ such that for 0?i?δ, where and ; (iv) there is no subspace W of V such that AW⊆W, A∗W⊆W, W≠0, W≠V. We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0?i?d the dimensions of coincide. The pair A,A∗ is called sharp whenever . It is known that if F is algebraically closed then A,A∗ is sharp. In this paper we classify up to isomorphism the sharp tridiagonal pairs. As a corollary, we classify up to isomorphism the tridiagonal pairs over an algebraically closed field. We obtain these classifications by proving the μ-conjecture. 相似文献
87.
A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for
- •
- nonderogatory complex matrices up to unitary similarity, and
- •
- pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues.
88.
Let f:N→N be a function. Let An=(aij) be the n×n matrix defined by aij=1 if i=f(j) for some i and j and aij=0 otherwise. We describe the Jordan canonical form of the matrix An in terms of the directed graph for which An is the adjacency matrix. We discuss several examples including a connection with the Collatz 3n+1 conjecture. 相似文献
89.
Nadine Große 《Differential Geometry and its Applications》2011,29(6):838-849
We prove the Hijazi inequality, an estimate for Dirac eigenvalues, for complete manifolds of finite volume. Under some additional assumptions on the dimension and the scalar curvature, this inequality is also valid for elements of the essential spectrum. This allows to prove the conformal version of the Hijazi inequality on conformally parabolic manifolds if the spin analog to the Yamabe invariant is positive. 相似文献
90.
We develop the concept of integral Menger curvature for a large class of nonsmooth surfaces. We prove uniform Ahlfors regularity and a C1,λ-a priori bound for surfaces for which this functional is finite. In fact, it turns out that there is an explicit length scale R>0 which depends only on an upper bound E for the integral Menger curvature Mp(Σ) and the integrability exponent p, and not on the surface Σ itself; below that scale, each surface with energy smaller than E looks like a nearly flat disc with the amount of bending controlled by the (local) Mp-energy. Moreover, integral Menger curvature can be defined a priori for surfaces with self-intersections or branch points; we prove that a posteriori all such singularities are excluded for surfaces with finite integral Menger curvature. By means of slicing and iterative arguments we bootstrap the Hölder exponent λ up to the optimal one, λ=1−(8/p), thus establishing a new geometric ‘Morrey–Sobolev’ imbedding theorem.As two of the various possible variational applications we prove the existence of surfaces in given isotopy classes minimizing integral Menger curvature with a uniform bound on area, and of area minimizing surfaces subjected to a uniform bound on integral Menger curvature. 相似文献