摘要:

The geometry of differential equations and their higher symmetries is studied by using spaces of jets of submanifolds. The geodesic equationgintroduced in this framework is proved to be a third order polynomial with respect to first derivatives. Contact symmetries of this equation are discussed. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814732

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

In this report, we consider doubly warped product manifolds and we get fundamental properties of this manifold and consider these submanifolds. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814733

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

In the present paper we study Einstein Lagrangian submanifolds. We show that ifMis a complete Einstein Lagrangian minimal submanifold of a complex projective spaceCPn(c), thenMis parallel andMis one of the following conditions holds: a)Mis totally geodesic, b)n= 2 andMis a finite Riemannian covering of a torus minimally embedded inCP2(c) with parallel second fundamental form, c)n> 2 andMis an embedded submanifold congruent to the standard embedding of:SU(3)/SO(3),n= 5;SU(3),n= 8;SU(6)/Sp(3),n= 14 orE6/F4,n= 26. We also study a compact Einstein Kaehler submanifold of a complex projective space. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814734

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Connections are among the most important tools to study qualitative features of dynamical systems. In this paper, we discuss generalized connections on affine bundles and show how they appear in the context of Lagrangian systems on affine Lie algebroids. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814735

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Constrained Hamiltonian systems are investigated by using Gu¨ler’s method. Integration of a set of equations of motion and the action function is discussed. It is shown that the canonical path integral quantization is obtained directly as an integration over the canonical phase‐space coordinates without any need to enlarge the initial phase‐space by introducing extra‐ unphysical variables as in the Batalin‐Fradkin‐Tyutin (BFT) method. The abelian Proca model is analyzed by the two methods. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814736

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

One proves that the Mazur‐Ulam theorem can be extended in the framework of metric spaces us long as a well behaved concept of midpoint is available. This leads to the new concept of Mazur‐Ulam space. Besides the classical case of real normed spaces, other examples such as Sym++(n,R), the space of alln × ndimensional positive definite matrices, appear as symmetric cones attached to Euclidean Jordan algebras. It turns out that the Mazur‐Ulam spaces provide a framework for new generalizations of the concept of convex function. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814737

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

LetGL(n,R) be the general linear group ofn × nreal matrices. Definitions ofGL(n,R)‐equivalence and the centro‐affine type of curves are introduced. All possible centro‐affine types are founded. For every centro‐affine type all invariant parametrizations of a curve are described. The problem ofGL(n,R)‐equivalence of curves is reduced to that of paths. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814738

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

Around 80 years ago, several authors (for instance H. Weyl, T.Y. Thomas, J. Douglas and J.H.C. Whitehead) studied the projective geometry of paths, using the methods of tensor calculus. The principal object of study was a spray, namely a homogeneous second‐order differential equation, or more generally a projective equivalence class of sprays. At around the same time, E. Cartan studied the same topic from a different point of view, by imagining a projective space attached to a manifold, or, more generally, attached to a ‘manifold of elements’; the infinitesimal ‘glue’ may be interpreted in modern language as a Cartan projective connection on a principal bundle. This paper describes the geometrical relationship between these two points of view. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814739

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

We study the analog of the Cauchy‐type integral for the Laplace vector fields theory in case of a piece‐wise Liapunov surface of integration and we prove the Sokhotski‐Plemelj theorem for it as well as the necessary and sufficient condition for the possibility to extend a given Ho¨lder function from such a surface up to a Laplace vector field. Formula for the square of the singular Cauchy‐type integral is given. The proofs of all these facts are based on intimate relations between Laplace vector held and some versions of quaternionic analysis. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814740

出版商:AIP    

年代:1904

数据来源: AIP

摘要:

In this paper we generalize the concept of a Lepage form, introduced by Krupka, to forms of arbitrary degree in mechanics. These forms allow us to find a suitable representation of the classes of forms, appearing in variational sequences in mechanics. The structure of Lepage 2‐forms is discussed in detail. The Lepage equivalents of the dynamical forms are mentioned. © 2004 American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.1814741

出版商:AIP    

年代:1904

数据来源: AIP