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)
Ivanov, S;
[1]
Zamkovoy, S
[2]
- University of Sofia 'St. Kl. Ohridski', Faculty of Mathematics and Informatics, Sofia (Bulgaria) and Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
- University of Sofia 'St. Kl. Ohridski', Faculty of Mathematics and Informatics, Sofia (Bulgaria)
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}
}
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}
}