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October 2009 On the canonical Hermitian connection in nearly Kähler manifolds
Luigi Vezzoni
Kodai Math. J. 32(3): 420-431 (October 2009). DOI: 10.2996/kmj/1257948887


In the present paper we prove that the Hermitian curvature tensor $\tilde{R}$ associated to a nearly Kähler metric g always satisfies the second Bianchi identity $\mathfrak{S}(\tilde{\nabla}_X\tilde{R})$ (Y, Z, ·, ·)=0 and that it satisfies the first Bianchi identity $\mathfrak{S}\tilde{R}$(X, Y, Z, ·)=0 if and only if g is a Kähler metric. Furthermore we characterize condition for $\tilde{R}$ to be parallel with respect to the canonical Hermitian connection $\tilde{\nabla}$ in terms of the Riemann curvature tensor and in the last part of the paper we study the curvature of some generalizations of the nearly Kähler structure.


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Luigi Vezzoni. "On the canonical Hermitian connection in nearly Kähler manifolds." Kodai Math. J. 32 (3) 420 - 431, October 2009.


Published: October 2009
First available in Project Euclid: 11 November 2009

zbMATH: 1180.53071
MathSciNet: MR2582009
Digital Object Identifier: 10.2996/kmj/1257948887

Rights: Copyright © 2009 Tokyo Institute of Technology, Department of Mathematics


Vol.32 • No. 3 • October 2009
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