Gray identities, canonical connection and integrability - Mathematics > Differential GeometryReport as inadecuate




Gray identities, canonical connection and integrability - Mathematics > Differential Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We characterize quasi K\-ahler manifolds whose curvature tensor associated tothe canonical Hermitian connection satisfies the first Bianchi identity. Thiscondition is related with the third Gray identity and in the almost K\-ahlercase implies the integrability. Our main tool is the existence of generalizedholomorphic frames introduced by the second author previously. By using suchframes we also give a simpler and shorter proof of a Theorem of Goldberg.Furthermore we study almost Hermitian structures having the curvature tensorassociated to the canonical Hermitian connection equal to zero. We show someexplicit examples of quasi K\-ahler structures on the Iwasawa manifold havingthe Hermitian curvature vanishing and the Riemann curvature tensor satisfyingthe second Gray identity.



Author: Antonio J. Di Scala, Luigi Vezzoni

Source: https://arxiv.org/



DOWNLOAD PDF




Related documents