منابع مشابه
Second-order Differential Equations and Nonlinear Connections
The main purposes of this article are to extend our previous results on homogeneous sprays [15] to arbitrary secondorder differential equations, to show that locally diffeomorphic exponential maps can be defined for any of them, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. In the process, we introduce vertically homogeneous connections. Unlike...
متن کاملEhresmann Connections, Exponential Maps, and Second-order Differential Equations
The main purpose of this article is to introduce a comprehensive, unified theory of the geometry of all connections. We show that one can study a connection via a certain, closely associated second-order differential equation. One of the most important results is our extended Ambrose-Palais-Singer correspondence. We extend the theory of geodesic sprays to certain second-order differential equat...
متن کاملSecond order structures for sprays and connections on Fréchet manifolds
Ambrose, Palais and Singer [6] introduced the concept of second order structures on finite dimensional manifolds. Kumar and Viswanath [23] extended these results to the category of Banach manifolds. In the present paper all of these results are generalized to a large class of Fréchet manifolds. It is proved that the existence of Christoffel and Hessian structures, connections, sprays and dissec...
متن کاملSemiholonomic Second Order Connections Associated with Material Bodies
The thermomechanical behavior of a material is expressed mathematically by means of one or more constitutive equations representing the response of the body to the history of its deformation and temperature. These settings induce a set of connections which can express local properties. We replace two of them by a second order connection and prove that the holonomity of this connection classifie...
متن کاملSecond-order Differential Equations, Exponential Maps, and Nonlinear Connections
The main purpose of this article is to introduce a comprehensive, unified theory of the geometry of all connections. We show that one can study any connection via a certain, closely associated second-order differential equation. One of the most important tools is our extended Ambrose-PalaisSinger correspondence. We extend the theory of geodesic sprays to arbitrary second-order differential equa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1972
ISSN: 0022-040X
DOI: 10.4310/jdg/1214431172