Abstract
A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs.
Galperin, A;
[1]
Ogievetsky, O;
[2]
Ivanov, E
- Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
- Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut
Citation Formats
Galperin, A, Ogievetsky, O, and Ivanov, E.
Harmonic space and quaternionic manifolds.
France: N. p.,
1992.
Web.
Galperin, A, Ogievetsky, O, & Ivanov, E.
Harmonic space and quaternionic manifolds.
France.
Galperin, A, Ogievetsky, O, and Ivanov, E.
1992.
"Harmonic space and quaternionic manifolds."
France.
@misc{etde_10109843,
title = {Harmonic space and quaternionic manifolds}
author = {Galperin, A, Ogievetsky, O, and Ivanov, E}
abstractNote = {A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs.}
place = {France}
year = {1992}
month = {Oct}
}
title = {Harmonic space and quaternionic manifolds}
author = {Galperin, A, Ogievetsky, O, and Ivanov, E}
abstractNote = {A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs.}
place = {France}
year = {1992}
month = {Oct}
}