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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. \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.
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