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Displaying similar documents to “< $> 𝒜 <$ >-Schemes and Zariski-Riemann Spaces”

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If $(M, \nabla)$ is a manifold with a symmetric linear connection, then $T^{*} M$ can be endowed with the natural Riemann extension $\bar{g}$ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to $\bar{g}$ initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure $𝒫$ on $(T^{*} M, \bar{g})$ and prove that $𝒫$ is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if $\bar{g}$ reduces...

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