scholarly journals Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle

2020 ◽  
pp. 595-600
Author(s):  
Rabia ÇAKAN AKPINAR
Keyword(s):  
Cotangent Bundle ◽  
Torsion Tensor ◽  
Riemannian Connection

scholarly journals Horizontal lifts from a manifold to its cotangent bundle

1967 ◽  
Vol 19 (2) ◽  
pp. 185-198 ◽  
Author(s):  
K. YANO ◽  
E. M. PATTERSON
Keyword(s):  
Cotangent Bundle

scholarly journals Affine varieties, singularities and the growth rate of wrapped Floer cohomology

2018 ◽  
Vol 10 (03) ◽  
pp. 493-530
Author(s):  
Mark McLean
Keyword(s):  
Growth Rate ◽  
Cotangent Bundle ◽  
Betti Numbers ◽  
Symplectic Manifolds ◽  
Isolated Singularity ◽  
Contact Manifolds ◽  
Floer Cohomology ◽  
Complex Singularities ◽  
Smooth Affine ◽  
Simply Connected

In this paper, we give partial answers to the following questions: Which contact manifolds are contactomorphic to links of isolated complex singularities? Which symplectic manifolds are symplectomorphic to smooth affine varieties? The invariant that we will use to distinguish such manifolds is called the growth rate of wrapped Floer cohomology. Using this invariant we show that if [Formula: see text] is a simply connected manifold whose unit cotangent bundle is contactomorphic to the link of an isolated singularity or whose cotangent bundle is symplectomorphic to a smooth affine variety then M must be rationally elliptic and so it must have certain bounds on its Betti numbers.

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.

scholarly journals A new class of metrics on the cotangent bundle

2020 ◽  
Vol 13(62) (1) ◽  
pp. 285-302
Author(s):  
Abderrahim Zagane ◽  
Keyword(s):  
Cotangent Bundle ◽  
New Class

scholarly journals Non-Smooth Geodesic Flows and Classical Mechanics

1969 ◽  
Vol 12 (2) ◽  
pp. 209-212 ◽  
Author(s):  
J. E. Marsden
Keyword(s):  
Phase Space ◽  
Kinetic Energy ◽  
Hamiltonian Systems ◽  
Configuration Space ◽  
Smooth Function ◽  
Cotangent Bundle ◽  
Classical Mechanics ◽  
Riemannian Metric ◽  
Geodesic Flows ◽  
Image Position

As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In fact, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q-space or the configuration space), we may define a smooth function Tg on the cotangent bundle T*M (q-p-space, or the phase space). This function is the kinetic energy of q, and locally is given by

scholarly journals On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

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