The GHP conformai Killing equations and their integrability conditions, with application to twisting type N vacuum spacetimes

1993 ◽  
Vol 25 (6) ◽  
pp. 625-651 ◽  
Author(s):  
Charalampos Kolassis ◽  
Garry Ludwig
Keyword(s):  
Integrability Conditions ◽  
Killing Equations

HOMOTHETIC KILLING VECTORS IN EXPANDING $\mathcal{HH}$-SPACES WITH Λ

2012 ◽  
Vol 10 (01) ◽  
pp. 1250077 ◽  
Author(s):  
ADAM CHUDECKI
Keyword(s):  
Master Equation ◽  
Killing Vector ◽  
Conformal Killing ◽  
Conformal Killing Vector ◽  
Killing Vectors ◽  
Type D ◽  
Integrability Conditions ◽  
Killing Equation ◽  
Killing Equations

Conformal Killing equations and their integrability conditions for expanding hyperheavenly spaces with Λ in spinorial formalism are studied. It is shown that any conformal Killing vector reduces to homothetic or isometric Killing vector. Reduction of respective Killing equation to one master equation is presented. Classification of homothetic and isometric Killing vectors is given. Type [D] ⊗ [any] is analyzed in detail and some expanding [Formula: see text] complex metrics of types [III, N] ⊗ [III, N] with Λ admitting isometric Killing vectors are found.

scholarly journals Second-order integrable Lagrangians and WDVV equations

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
E. V. Ferapontov ◽  
M. V. Pavlov ◽  
Lingling Xue
Keyword(s):  
Lagrangian Density ◽  
Theta Functions ◽  
Second Order ◽  
Elementary Functions ◽  
Lagrange Equations ◽  
Wdvv Equations ◽  
Integrability Conditions ◽  
Jacobi Theta Functions

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

GEOMETRICAL CONSTRAINTS FOR D = 10, N = 1 SUPERGRAVITY

1989 ◽  
Vol 04 (15) ◽  
pp. 3819-3831 ◽  
Author(s):  
LING-LIE CHAU ◽  
CHONG-SA LIM
Keyword(s):  
Equations Of Motion ◽  
Bianchi Identities ◽  
Dynamical Consequence ◽  
Integrability Conditions ◽  
Geometrical Constraints ◽  
Additional Constraints

A set of geometrical constraints for D = 10, N = 1 supergravity is formulated. It has the meaning as integrability conditions on "hyperplanes" determined by light-like lines in the superspace. The dynamical consequence of these geometrical constraints is studied via Bianchi identities. Since no equations of motion have resulted, these geometrical constraints can form an off-shell set of constraints for the theory. We also discuss additional constraints that lead to Poincare supergravity equations of motion. The relation of the theory with D = 4 N = 4 supergravity is also illuminated.

On the spectrum and the distribution of singular values of Schrödinger operators with a complex potential

1983 ◽  
Vol 388 (1794) ◽  
pp. 195-218 ◽  
Keyword(s):  
Complex Potential ◽  
Spectral Properties ◽  
Polynomial Growth ◽  
Schrödinger Operators ◽  
Singular Values ◽  
Negative Real Part ◽  
Adjoint Problem ◽  
Schrodinger Operators ◽  
Asymptotic Estimates ◽  
Integrability Conditions

This paper is concerned with spectral properties of the Schrödinger operator ─ ∆+ q with a complex potential q which has non-negative real part and satisfies weak integrability conditions. The problem is dealt with as a genuine non-self-adjoint problem, not as a perturbation of a self-adjoint one, and global and asymptotic estimates are obtained for the corresponding singular values. From these estimates information is obtained about the eigenvalues of the problem. By way of illustration, detailed calculations are given for an example in which the potential has at most polynomial growth.

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