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Harmonic space and quaternionic manifolds

Technical Report:

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.
Authors:
Galperin, A; [1]  Ogievetsky, O; [2]  Ivanov, E
  1. Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
  2. Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut
Publication Date:
Oct 01, 1992
Product Type:
Technical Report
Report Number:
LAPP-L-405-92
Reference Number:
SCA: 662120; PA: AIX-25:004076; EDB-94:015680; ERA-19:005600; NTS-94:014779; SN: 93001121053
Resource Relation:
Other Information: PBD: Oct 1992
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; MATHEMATICAL SPACE; SUPERSYMMETRY; GEOMETRY; MATHEMATICAL MANIFOLDS; SIGMA MODEL; SP GROUPS; SU-2 GROUPS; SUPERGRAVITY; 662120; SYMMETRY, CONSERVATION LAWS, CURRENTS AND THEIR PROPERTIES
OSTI ID:
10109843
Research Organizations:
Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules Elementaires
Country of Origin:
France
Language:
English
Other Identifying Numbers:
Other: ON: DE94609639; TRN: FR9303128004076
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
FRN
Size:
44 p.
Announcement Date:
Jun 30, 2005

Technical Report:

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}
}