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@article{1642397,
author = {Borówka, Aleksandra Wiktoria and Winther, Henrik},
article_location = {Springer P.O. AH Dordrecht},
article_number = {3},
doi = {http://dx.doi.org/10.1007/s10455-018-9631-3},
keywords = {c-projective structure; Quaternionic structure; Symmetries; Submaximally symmetric spaces; Calabi metric},
language = {eng},
issn = {0232-704X},
journal = {Annals of Global Analysis and Geometry},
title = {C-projective symmetries of submanifolds in quaternionic geometry},
url = {https://link.springer.com/article/10.1007/s10455-018-9631-3},
volume = {55},
year = {2019}
}
TY - JOUR
ID - 1642397
AU - Borówka, Aleksandra Wiktoria - Winther, Henrik
PY - 2019
TI - C-projective symmetries of submanifolds in quaternionic geometry
JF - Annals of Global Analysis and Geometry
VL - 55
IS - 3
SP - 395-416
EP - 395-416
PB - Springer
SN - 0232704X
KW - c-projective structure
KW - Quaternionic structure
KW - Symmetries
KW - Submaximally symmetric spaces
KW - Calabi metric
UR - https://link.springer.com/article/10.1007/s10455-018-9631-3
L2 - https://link.springer.com/article/10.1007/s10455-018-9631-3
N2 - The generalized Feix-Kaledin construction shows that c-projective 2n-manifolds with curvature of type (1,1) are precisely the submanifolds of quaternionic 4n-manifolds which are fixed-point set of a special type of quaternionic circle action. In this paper, we consider this construction in the presence of infinitesimal symmetries of the two geometries. First, we prove that the submaximally symmetric c-projective model with type (1,1) curvature is a submanifold of a submaximally symmetric quaternionic model and show how this fits into the construction. We give conditions for when the c-projective symmetries extend from the fixed-point set of the circle action to quaternionic symmetries, and we study the quaternionic symmetries of the Calabi and Eguchi-Hanson hyperkahler structures, showing that in some cases all quaternionic symmetries are obtained in this way.
ER -
BORÓWKA, Aleksandra Wiktoria a Henrik WINTHER. C-projective symmetries of submanifolds in quaternionic geometry. Online. \textit{Annals of Global Analysis and Geometry}. Springer P.O. AH Dordrecht: Springer, 2019, roč.~55, č.~3, s.~395-416. ISSN~0232-704X. Dostupné z: https://dx.doi.org/10.1007/s10455-018-9631-3. [citováno 2024-04-24]
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