scholarly journals Lie derivatives of almost contact structure and almost paracontact structure with respect to X^{C} and X^{V} on Tangent Bundle T(M)

2016 ◽  
Vol 4 (1) ◽  
pp. 153-153 ◽  
Author(s):  
Hasim Cayir ◽  
Gokhan Koseoglu
Keyword(s):  
Tangent Bundle ◽  
Contact Structure ◽  
Almost Contact Structure ◽  
Lie Derivatives ◽  
Derivatives Of ◽  
Almost Paracontact Structure

ON FINSLER MANIFOLDS WHOSE TANGENT BUNDLE HAS THE g-NATURAL METRIC

2011 ◽  
Vol 08 (07) ◽  
pp. 1593-1610 ◽  
Author(s):  
ESMAEIL PEYGHAN ◽  
AKBAR TAYEBI
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Positive Constant ◽  
Tangent Bundle ◽  
Contact Structure ◽  
Jacobi Operator ◽  
Riemannian Metric ◽  
Finsler Manifolds ◽  
Almost Contact Structure ◽  
Flat Riemannian Manifold

In this paper, we introduce a Riemannian metric [Formula: see text] and a family of framed f-structures on the slit tangent bundle [Formula: see text] of a Finsler manifold Fn = (M, F). Then we prove that there exists an almost contact structure on the tangent bundle, when this structure is restricted to the Finslerian indicatrix. We show that this structure is Sasakian if and only if Fn is of positive constant curvature 1. Finally, we prove that (i) Fn is a locally flat Riemannian manifold if and only if [Formula: see text], (ii) the Jacobi operator [Formula: see text] is zero or commuting if and only if (M, F) have the zero flag curvature.

scholarly journals On the existence of almost contact structure and the contact magnetic field

2009 ◽  
Vol 125 (1-2) ◽  
pp. 191-199 ◽  
Author(s):  
J. L. Cabrerizo ◽  
M. Fernández ◽  
J. S. Gómez
Keyword(s):  
Magnetic Field ◽  
Contact Structure ◽  
Almost Contact Structure

Infinitesimal Deformations of ECD Fields

2020 ◽  
pp. 147-154
Author(s):  
Daniel Canarutto
Keyword(s):  
Lie Derivative ◽  
Dirac Fields ◽  
Lie Derivatives ◽  
Infinitesimal Deformations ◽  
Standard Notion ◽  
Derivatives Of

The standard notion of Lie derivative is extended in order to include Lie derivatives of spinors, soldering forms, spinor connections and spacetime connections. These extensions are all linked together, and provide a natural framework for discussing infinitesimal deformations of Einstein-Cartan-Dirac fields in the tetrad-affine setting.

scholarly journals Lie derivatives of sectorform fields

1988 ◽  
Vol 55 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Ivan Kolář
Keyword(s):  
Lie Derivatives ◽  
Derivatives Of

Normal Variations of Invariant Hypersurfaces of Framed Manifolds

1972 ◽  
Vol 15 (4) ◽  
pp. 513-521
Author(s):  
Samuel I. Goldberg
Keyword(s):  
Complex Manifold ◽  
Contact Structure ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Marked Contrast ◽  
Almost Complex Manifold ◽  
Almost Contact Structure ◽  
Almost Complex ◽  
Differentiable Vector ◽  
Real Codimension

A hypersurface of a globally framed f-manifold (briefly, a framed manifold), does not in general possess a framed structure as one may see by considering the 4-sphere S4 in R5 or S5. For, a hypersurface so endowed carries an almost complex structure, or else, it admits a nonsingular differentiable vector field. Since an almost complex manifold may be considered as being globally framed, with no complementary frames, this situation is in marked contrast with the well known fact that a hypersurface (real codimension 1) of an almost complex manifold admits a framed structure, more specifically, an almost contact structure.

scholarly journals Spinor Lie derivatives and Fermion stress–energies

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150757
Author(s):  
A. D. Helfer
Keyword(s):  
Discrete Symmetries ◽  
Vector Fields ◽  
Lie Derivative ◽  
General Covariance ◽  
Arbitrary Vector ◽  
Lie Derivatives ◽  
Spinor Fields ◽  
Stress Energy ◽  
Derivatives Of ◽  
Apparent Conflict

Stress–energies for Fermi fields are derived from the principle of general covariance. This is done by developing a notion of Lie derivatives of spinors along arbitrary vector fields. A substantial theory of such derivatives was first introduced by Kosmann; here, I show how an apparent conflict in the literature on this is due to a difference in the definitions of spinors, and that tracking the Lie derivative of the Infeld–van der Waerden symbol, as well as the spinor fields under consideration, gives a fuller picture of the geometry and leads to the Fermion stress–energy. The differences in the definitions of spinors do not affect the results here, but could matter in certain quantum-gravity programs and for spinor transformations under discrete symmetries.

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