Counting holomorphic connections with a prescribed Ricci tensor

Jan Kurek, Włodzimierz Mikulski, Mariusz Plaszczyk

Abstract


How many holomorphic connections are there with a prescribed Ricci tensor? How many torsion-free holomorphic connections are there with a prescribed Ricci tensor? These questions are answered by using the holomorphic version of the Cauchy–Kowalevski theorem.

Keywords


Holomorphic connection; Ricci tensor; holomorphic version of the Cauchy-Kowalevski theorem

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References


DeTurck, D., Existence of metrics with prescribed Ricci curvature: local theory, Invent. Math. 65 (1981), 179–207.

DeTurck, D., Norito, K., Uniqueness and non-existence of metrics with prescribed Ricci curvature, Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1984), 351–359.

Dusek, Z., Kowalski, O., How many are Ricci flat affine connections with arbitrary torsion, Publ. Math. Debrecen 88 (2016), 511–516.

Gantumur, T., The Cauchy–Kovalevskaya Theorem, Math 580, Lecture Notes 2, 2011.

Gasqui, J., Connexions a courbure de Ricci donnee, Math. Z. 168 (1979), 167–179.

Gasqui, J., Sur la courbure de Ricci d’une connexion lineaire, C. R. Acad. Sci. Paris Ser A-B 281 (1975), 389–391.

Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Volume II, Interscience Publishers, New York, 1969.

Kurek, J., Mikulski, W. M., Plaszczyk, M., How many are projectable classical linear connections with a prescribed Ricci tensor, Filomat 35 (10) (2022), 3279–3285.

Opozda, B., Mikulski, W. M., The Cauchy–Kowalevski theorem applied for counting connections with a prescribed Ricci tensor, Turkish J. Math. 42 (2018), 528–536.




DOI: http://dx.doi.org/10.17951/a.2023.77.1.25-34
Date of publication: 2023-09-30 21:35:45
Date of submission: 2023-09-26 21:22:15


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