scholarly journals On Pull-Back Bundle of Tensor Bundles Defined by Projection of The Cotangent Bundle

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Furkan Yildirim
Keyword(s):  
Special Class ◽  
Cotangent Bundle ◽  
Vector Fields ◽  
Complete Lift ◽  
Tensor Bundle

AbstractUsing projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The aim of this study is to investigate complete lift of vector fields in a special class of semi-tensor bundle tM of the type (p,q). We also have a new example for good square in this work.

scholarly journals SOME NOTES ON THE MODIFIED RIEMANNIAN EXTENSION g ̃_(∇,c) ON COTANGENT BUNDLE

2020 ◽  
Vol 20 (4) ◽  
pp. 931-940
Author(s):  
HASIM CAYIR
Keyword(s):  
Cotangent Bundle ◽  
Vector Fields ◽  
Lie Derivatives ◽  
Complete And Vertical Lifts

In this paper, we define the modified Riemannian extension g ̃_(∇,c) in the cotangent bundle T^* M, which is completely determined by its action on complete lifts of vector fields. Later, we obtain the covarient and Lie derivatives applied to the modified Riemannian extension with respect to the complete and vertical lifts of vector and kovector fields, respectively.

COMPLETE LIFT OF F(K-(K-2))-STRUCTURE IN COTANGENT BUNDLE

1981 ◽  
Vol 14 (1) ◽  
Author(s):  
V. C. Gupta ◽  
Renu Dubey
Keyword(s):  
Cotangent Bundle ◽  
Complete Lift

PROPER PROJECTIVE SYMMETRY IN SPHERICALLY SYMMETRIC STATIC SPACE–TIMES

2005 ◽  
Vol 14 (08) ◽  
pp. 1451-1463 ◽  
Author(s):  
GHULAM SHABBIR ◽  
M. AMER QURESHI
Keyword(s):  
Special Class ◽  
Vector Fields ◽  
Space Time ◽  
Spherically Symmetric ◽  
Direct Integration ◽  
Integration Techniques ◽  
Projective Vector ◽  
Static Space

A study of proper projective symmetry in spherically symmetric static space–times is given by using algebraic and direct integration techniques. It is shown that a special class of the above space–time admits proper projective vector fields.

scholarly journals Complete lift of vector fields and sprays to T∞M

2015 ◽  
Vol 12 (10) ◽  
pp. 1550113 ◽  
Author(s):  
Ali Suri ◽  
Somaye Rastegarzadeh
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Dimensional Manifold ◽  
Closed Curves ◽  
Infinite Dimensional ◽  
Integral Curves ◽  
Complete Lift ◽  
Infinite Dimensional Manifold

In this paper for a given Banach, possibly infinite dimensional, manifold M we focus on the geometry of its iterated tangent bundle TrM, r ∈ ℕ ∪ {∞}. First we endow TrM with a canonical atlas using that of M. Then the concepts of vertical and complete lifts for functions and vector fields on TrM are defined which they will play a pivotal role in our next studies i.e. complete lift of (semi)sprays. Afterward we supply T∞M with a generalized Fréchet manifold structure and we will show that any vector field or (semi)spray on M, can be lifted to a vector field or (semi)spray on T∞M. Then, despite of the natural difficulties with non-Banach modeled manifolds, we will discuss about the ordinary differential equations on T∞M including integral curves, flows and geodesics. Finally, as an example, we apply our results to the infinite-dimensional case of manifold of closed curves.

scholarly journals TWO-DIMENSIONAL INTERACTIONS BETWEEN A BF-TYPE THEORY AND A COLLECTION OF VECTOR FIELDS

2004 ◽  
Vol 19 (24) ◽  
pp. 4101-4125 ◽  
Author(s):  
E. M. CIOROIANU ◽  
S. C. SĂRARU
Keyword(s):  
Gauge Theory ◽  
Type Theory ◽  
Special Class ◽  
Vector Fields ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Lagrangian Action ◽  
Deformation Procedure

Consistent interactions that can be added to a two-dimensional, free Abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. The deformation procedure modifies the Lagrangian action, the gauge transformations, as well as the accompanying algebra of the interacting model.

scholarly journals $\vee$ -Systems, Holonomy Lie Algebras, and Logarithmic Vector Fields

2017 ◽  
Vol 2018 (7) ◽  
pp. 2070-2098 ◽  
Author(s):  
Misha V Feigin ◽  
Alexander P Veselov
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Special Class ◽  
Vector Fields ◽  
Hyperplane Arrangement ◽  
Gradient Vector ◽  
Coxeter Systems ◽  
Flat Coordinates

Abstract It is shown that the description of certain class of representations of the holonomy Lie algebra $\mathfrak g_{\Delta}$ associated with hyperplane arrangement $\Delta$ is essentially equivalent to the classification of $\vee$-systems associated with $\Delta.$ The flat sections of the corresponding $\vee$-connection can be interpreted as vector fields, which are both logarithmic and gradient. We conjecture that the hyperplane arrangement of any $\vee$-system is free in Saito's sense and show this for all known $\vee$-systems and for a special class of $\vee$-systems called harmonic, which includes all Coxeter systems. In the irreducible Coxeter case the potentials of the corresponding gradient vector fields turn out to be Saito flat coordinates, or their one-parameter deformations. We give formulas for these deformations as well as for the potentials of the classical families of harmonic $\vee$-systems.

Sign in / Sign up

Export Citation Format

Share Document