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Para-Hermitian and para-quaternionic manifolds

Abstract

A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S{sup 1} x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)
Authors:
Ivanov, S; [1]  Zamkovoy, S [2] 
  1. University of Sofia 'St. Kl. Ohridski', Faculty of Mathematics and Informatics, Sofia (Bulgaria) and Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
  2. University of Sofia 'St. Kl. Ohridski', Faculty of Mathematics and Informatics, Sofia (Bulgaria)
Publication Date:
Oct 01, 2003
Product Type:
Technical Report
Report Number:
IC-2003/145
Resource Relation:
Other Information: 59 refs
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAUCHY PROBLEM; CONFORMAL GROUPS; GENERAL RELATIVITY THEORY; HERMITIAN OPERATORS; METRICS; RIEMANN SPACE; SMOOTH MANIFOLDS; SO-2 GROUPS; SU-2 GROUPS; TENSORS; U-1 GROUPS
OSTI ID:
20702945
Research Organizations:
Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: Contract MM 809/1998; 586/2002; HPRN-CT-2000-00101; TRN: XA0502769018092
Availability:
Available from INIS in electronic form; Also available at: http://www.ictp.it
Submitting Site:
INIS
Size:
30 pages
Announcement Date:
Apr 07, 2006

Citation Formats

Ivanov, S, and Zamkovoy, S. Para-Hermitian and para-quaternionic manifolds. IAEA: N. p., 2003. Web.
Ivanov, S, & Zamkovoy, S. Para-Hermitian and para-quaternionic manifolds. IAEA.
Ivanov, S, and Zamkovoy, S. 2003. "Para-Hermitian and para-quaternionic manifolds." IAEA.
@misc{etde_20702945,
title = {Para-Hermitian and para-quaternionic manifolds}
author = {Ivanov, S, and Zamkovoy, S}
abstractNote = {A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S{sup 1} x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)}
place = {IAEA}
year = {2003}
month = {Oct}
}