Covariant derivatives of a spinor in finsler geometry

1973 ◽  
Vol 16 (2) ◽  
pp. 171-176
Author(s):  
V. P. Sevryuk
Keyword(s):  
Finsler Geometry ◽  
Covariant Derivatives ◽  
Derivatives Of

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

Conformai Curvature Tensors

2011 ◽  
Author(s):  
Charles Fefferman ◽  
C. Robin Graham
Keyword(s):  
Normal Form ◽  
Curvature Tensor ◽  
Riemannian Metric ◽  
Conformal Group ◽  
Conformal Change ◽  
Conformal Curvature ◽  
Covariant Derivatives ◽  
Curvature Tensors ◽  
Derivatives Of

This chapter studies conformal curvature tensors of a pseudo-Riemannian metric g. These are defined in terms of the covariant derivatives of the curvature tensor of an ambient metric in normal form relative to g. Their transformation laws under conformal change are given in terms of the action of a subgroup of the conformal group O(p + 1, q + 1) on tensors. It is assumed throughout this chapter that n ≥ 3.

scholarly journals On higher covariant derivatives of the curvature tensors of Kählerian C-spaces

1983 ◽  
Vol 91 ◽  
pp. 1-18 ◽  
Author(s):  
Ryoichi Takagi
Keyword(s):  
Symmetric Spaces ◽  
Compact Type ◽  
Hermitian Symmetric Spaces ◽  
Covariant Derivatives ◽  
Higher Covariant Derivatives ◽  
Group Of Isometries ◽  
Complex Homogeneous Manifold ◽  
Curvature Tensors ◽  
Simply Connected ◽  
Derivatives Of

A compact simply connected complex homogeneous manifold is said briefly a C-space, which was completely classified by H. C. Wang [12]. A C-space is called to be Kählerian if it admits a Kählerian metric such that a group of isometries acts transitively on it. Hermitian symmetric spaces of compact type are typical examples of a Kählerian C-space. Let M be an arbitrary Kählerian C-space and R its curvature tensor. M. Itoh [6] expressed R in the language of Lie algebra and investigated various properties of R. In this paper, we study higher covariant derivatives of R.

scholarly journals Minimal coupling in presence of non-metricity and torsion

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Adrià Delhom
Keyword(s):  
Riemannian Space ◽  
Field Equations ◽  
Lagrange Equations ◽  
Minimal Coupling ◽  
Covariant Derivatives ◽  
Derivatives Of ◽  
Matter Fields

Abstract We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution $$\partial \rightarrow \nabla $$∂→∇ introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler–Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the associated Noether currents and charges. Then we will see that if the minimal coupling prescriptions is applied as we discuss, for spin 0 and 1 fields the results of MCPL and MCPF are equivalent, while for spin 1/2 fields there is a difference if one applies the MCPF or the MCPL, since the former leads to charge violation.

Сurvature-torsion tensor for Cartan connection

2019 ◽  
pp. 155-168
Author(s):  
Yu. Shevchenko
Keyword(s):  
Homogeneous Space ◽  
Lie Group ◽  
Principal Bundle ◽  
Torsion Tensor ◽  
Projective Connection ◽  
Cartan Connection ◽  
Bianchi Identities ◽  
Covariant Derivatives ◽  
Structure Equations ◽  
Derivatives Of

A Lie group containing a subgroup is considered. Such a group is a principal bundle, a typical fiber of this principal bundle is the subgroup and a base is a homogeneous space, which is obtained by factoring the group by the subgroup. Starting from this group, we constructed structure equations of a space with Cartan connection, which generalizes the Cartan point projective connection, Akivis’s linear projective connection, and a plane projective connection. Structure equations of this Cartan connection, containing the components of the curvature-torsion object, allowed: 1) to show that the curvature-torsion object forms a tensor containing a torsion tensor; 2) to find an analogue of the Bianchi identities such that the curvature-torsion tensor and its Pfaff derivatives satisfy this analogue; 3) to obtain the conditions for the transformation of Pfaffian derivatives of the curvature-torsion tensor into covariant derivatives with respect to the Cartan connection.

scholarly journals Computational Algorithm for Covariant Series Expansions in General Relativity

2018 ◽  
Vol 173 ◽  
pp. 03021 ◽  
Author(s):  
Ivan Potashov ◽  
Alexander Tsirulev
Keyword(s):  
Tensor Field ◽  
Computational Algorithm ◽  
Series Expansions ◽  
Tensor Fields ◽  
Normal Coordinates ◽  
Covariant Derivatives ◽  
Taylor Polynomials ◽  
Real Analytic ◽  
Derivatives Of ◽  
Torsion Free

We present a new algorithm for computing covariant power expansions of tensor fields in generalized Riemannian normal coordinates, introduced in some neighborhood of a parallelized k-dimensional submanifold (k = 0, 1, . . .< n; the case k = 0 corresponds to a point), by transforming the expansions to the corresponding Taylor series. For an arbitrary real analytic tensor field, the coefficients of such series are expressed in terms of its covariant derivatives and covariant derivatives of the curvature and the torsion. The algorithm computes the corresponding Taylor polynomials of arbitrary orders for the field components and is applicable to connections that are, in general, nonmetric and not torsion-free. We show that this computational problem belongs to the complexity class LEXP.

Differential invariants of the metric field and a 1-form

2016 ◽  
Vol 13 (10) ◽  
pp. 1650125
Author(s):  
Zdeněk Dušek
Keyword(s):  
Curvature Tensor ◽  
Proper Subgroup ◽  
Second Order ◽  
Differential Invariants ◽  
Covariant Derivatives ◽  
Differential Group ◽  
Derivatives Of

Second-order differential invariants of the metric field [Formula: see text] and a [Formula: see text]-form [Formula: see text] on the manifold are described using the factorization of the differential group with respect to a proper subgroup. It is proved that, all these invariants depend on the metric, its curvature tensor and covariant derivatives of the [Formula: see text]-form.

Spin gauge field theory of electric and magnetic spinors

1981 ◽  
Vol 377 (1768) ◽  
pp. 1-23 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Gauge Theory ◽  
Gauge Field Theory ◽  
Spin Space ◽  
Conjugation Operator ◽  
Vector Potentials ◽  
Covariant Derivatives ◽  
Component Theory ◽  
Curvature And Torsion ◽  
Derivatives Of

In the first section, a gauge theory of an unquantized generalized electron interacting with the electromagnetic field through two vector potentials is formulated, based on invariance of the Lagrangian under an algebra of spin space transformations. The covariant derivative is essentially expres­sed in terms of spin space operators. It is not possible to define dual monopole spinors in a four-component theory. However, a modified eight-component generalized electron gauge theory transforms into a dual monopole theory by using a square root of the charge conjugation operator. The covariant derivatives of the two spinors are members of a continuous set, and define curvature and torsion in spin space corresponding to the two spinors. Physically important ‘weak spin curvature’ is closely related to the total electromagnetic field. Possible physical interpretations and extensions of the theory are discussed.

VERTEX OPERATORS FOR THE CLOSED BOSONIC STRING THEORY AT ARBITRARY GENUS IN THE OPERATOR FORMALISM

1990 ◽  
Vol 05 (12) ◽  
pp. 2391-2409 ◽  
Author(s):  
ADRIAN R. LUGO
Keyword(s):  
String Theory ◽  
Bosonic String ◽  
Integral Approach ◽  
Vertex Operators ◽  
Operator Formalism ◽  
Covariant Derivatives ◽  
Bosonic String Theory ◽  
Dilaton Coupling ◽  
Derivatives Of ◽  
Closed Bosonic String

A systematic procedure for constructing vertex operators for the physical states of the closed bosonic string theory at genus g in the operator formalism is presented. The method is based on imposing suitable commutation relations with the generators of the conformal transformations required by unitarity of scattering amplitudes. An Arakelov-type metric on the Riemann surface naturally arises in the case of the tachyon, which allows to define vertex operators at higher levels via covariant derivatives. They involve covariant derivatives of the curvature with respect to this metric as it happens in the path integral approach. As a particular result, the Fradkin-Tseytlin dilaton coupling is obtained.

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