187 research outputs found
Covariant symplectic structure of the complex Monge-Amp\`ere equation
The complex Monge-Amp\`ere equation admits covariant bi-symplectic structure
for complex dimension 3, or higher. The first symplectic 2-form is obtained
from a new variational formulation of complex Monge- Amp\`ere equation in the
framework of the covariant Witten-Zuckerman approach to symplectic structure.
We base our considerations on a reformulation of the Witten-Zuckerman theory in
terms of holomorphic differential forms. The first closed and conserved
Witten-Zuckerman symplectic 2-form for the complex Monge-Amp\`ere equation is
obtained in arbitrary dimension and for all cases elliptic, hyperbolic and
homogeneous.
The connection of the complex Monge-Amp\`ere equation with Ricci-flat
K\"ahler geometry suggests the use of the Hilbert action. However, we point out
that Hilbert's Lagrangian is a divergence for K\"ahler metrics. Nevertheless,
using the surface terms in the Hilbert Lagrangian we obtain the second
Witten-Zuckerman symplectic 2-form for complex dimension>2.Comment: Physics Letters A 268 (2000) 29
A theorem on topologically massive gravity
We show that for three dimensional space-times admitting a hypersurface
orthogonal Killing vector field Deser, Jackiw and Templeton's vacuum field
equations of topologically massive gravity allow only the trivial flat
space-time solution. Thus spin is necessary to support topological mass.Comment: published in Classical and Quantum Gravity 13 (1996) L2
Electrovac -waves
New exact solutions of the Einstein-Maxwell field equations that describe
-waves are presented
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