Abstract
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
Jaime Muñoz-Masqué, maestro y amigo, en su 65 aniversario
Dedicated to Muñoz-Masqué, teacher and friend, on his 65th birth anniversary.
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- 1.
This is not a great loss of generality in view of the existence of the vector bundle isomorphism \({\textit{TM}}\rightarrow E\), between \({\textit{TM}}\) and the Batchelor bundle, already mentioned in the Introduction (see [13]), so the changes needed to deal with the most general case are mainly notational.
- 2.
In a technical sense that we will not describe here. See [12] for the details.
- 3.
In particular,
is not a tensor, hence the difference in notation.
is not a tensor, hence the difference in notation.References
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Acknowledgments
JM was supported by a Spanish Ministry of Science and Innovation project code MTM2012-33073. JV was supported by a CONACyT (México) project code CB-2012-179115.
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Hernández-Amador, R., Monterde, J., Vallejo, J. (2016). Supermanifolds, Symplectic Geometry and Curvature. In: Castrillón López, M., Hernández Encinas, L., Martínez Gadea, P., Rosado María, M. (eds) Geometry, Algebra and Applications: From Mechanics to Cryptography. Springer Proceedings in Mathematics & Statistics, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-319-32085-4_12
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