Infinitesimal rigidity and flexibility of a non-symmetric affine connection space
نویسندگان
چکیده
At the present work we consider infinitesimal deformations f : x → x + εz(x) of a space LN with non-symmetric affine connection L i jk . Based on the non-symmetry of the connection, we use four kinds of covariant derivative to express the Lie derivative and the deformations. Rigidity of geometric objects (connection, tensors, curvature) is defined by virtue of Lie derivative. AMS Subj. Class.: 53C25, 53A45, 53B05
منابع مشابه
Infinitesimal Affine Automorphisms of Symplectic Connections
Conditions are given under which an infinitesimal automorphism of a torsion-free connection preserving a symplectic form is necessarily a symplectic vector field. An example is given of a compact symplectic nilmanifold admitting a flat symplectic connection and an infinitesimal automorphism that is not symplectic. On a symplectic manifold (M,Ω), a symplectic connection is a torsion-free affine ...
متن کاملOn Ricci Type Identities in Manifolds with Non-symmetric Affine Connection
In [18], using polylinear mappings, we obtained several curvature tensors in the space LN with non-symmetric affine connection ∇. By the same method, we here examine Ricci type identities.
متن کاملInjective and non-injective realizations with symmetry
In this paper, we introduce a natural classification of bar and joint frameworks that possess symmetry. This classification establishes the mathematical foundation for extending a variety of results in rigidity, as well as infinitesimal or static rigidity, to frameworks that are realized with certain symmetries and whose joints may or may not be embedded injectively in the space. In particular,...
متن کاملThe Orbit Rigidity Matrix of a Symmetric Framework
A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix repres...
متن کاملInfinite bar-joint frameworks, crystals and operator theory
A theory of flexibility and rigidity is developed for general infinite bar-joint frameworks (G, p). Determinations of nondeformability through vanishing flexibility are obtained as well as sufficient conditions for deformability. Forms of infinitesimal flexibility are defined in terms of the operator theory of the associated infinite rigidity matrix R(G, p). The matricial symbol function of an ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 31 شماره
صفحات -
تاریخ انتشار 2010