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On products of generalized geometries

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Abstract

In this paper we address what generalized geometric structures are possible on products of spaces that each admit generalized geometries. In particular we consider, first, the product of two odd dimensional spaces that each admit a generalized almost contact structure, and then subsequently, the product of an odd dimensional space that admits a generalized almost contact structure and an even dimensional space that admits a generalized almost complex structure. We also draw attention to the relationship of the Courant bracket to the classical notion of normality for almost contact structures.

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Acknowledgments

We thank Charles P. Boyer for useful conversations. The second author thanks the Courant Institute for Mathematical Sciences for their hospitality during the work on this paper. Both authors would like to thank the referee for helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA, 19081, USA

    Ralph R. Gomez & Janet Talvacchia

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  1. Ralph R. Gomez
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  2. Janet Talvacchia
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Correspondence to Ralph R. Gomez.

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Gomez, R.R., Talvacchia, J. On products of generalized geometries. Geom Dedicata 175, 211–218 (2015). https://doi.org/10.1007/s10711-014-0036-6

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  • DOI: https://doi.org/10.1007/s10711-014-0036-6

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