Complete lift of a tensor field of type (1,2) to semi-cotangent 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.

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The hidden scalar Lagrangians within Horndeski theory

International Journal of Modern Physics D ◽

10.1142/s021827182043004x ◽

2020 ◽

Vol 29 (14) ◽

pp. 2043004

Author(s):

Gregory W. Horndeski

Keyword(s):

Scalar Field ◽

Generating Function ◽

Cotangent Bundle ◽

Tensor Field ◽

Scalar Fields ◽

Field Theories ◽

Metric Tensor ◽

Cosmological Solutions ◽

Different Types ◽

Vacuum Solutions

In this paper, I show that there exists a new way to obtain scalar–tensor field theories by combining a special scalar field on the cotangent bundle with a scalar field on spacetime. These two scalar fields act as a generating function for the metric tensor. When using these two scalar fields in the Horndeski Lagrangians, we discover, while seeking Friedmann–Lemaître–Robertson–Walker-type cosmological solutions, that hidden in the Horndeski Lagrangians are nondegenerate second-order scalar Lagrangians. In accordance with Ostrogradsky’s work, these hidden scalar Lagrangians lead to multiple vacuum solutions, and thereby predict the existence of the multiverse. The multiverse is comprised of numerous different types of individual universes. For example, some begin explosively, and then coast along exponentially forever at an accelerated rate, while others begin in that manner, and then stop expanding and contract.

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On Complete lift and Nijenhuis tensor of (1,1) tensorfield of the Basespace in the Cotangent Bundle

IOSR Journal of Mathematics ◽

10.9790/5728-0452426 ◽

2013 ◽

Vol 4 (5) ◽

pp. 24-26

Author(s):

Ram Nivas Ram Nivas

Keyword(s):

Cotangent Bundle ◽

Nijenhuis Tensor ◽

Complete Lift

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Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽

10.3390/sym13050830 ◽

2021 ◽

Vol 13 (5) ◽

pp. 830

Author(s):

Evgeniya V. Goloveshkina ◽

Leonid M. Zubov

Keyword(s):

Nonlinear Theory ◽

Hollow Sphere ◽

Tensor Field ◽

Exact Analytical Solution ◽

Symmetric Tensor ◽

Symmetric Distribution ◽

Spherically Symmetric ◽

Tensor Fields ◽

Spherically Symmetric Distribution ◽

Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

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