On the canonical Hermitian connection in nearly Kähler manifolds

Kodai Mathematical Journal

Luigi Vezzoni¹ 

[1] Dipartimento di Matematica Università di Torino

关键词: Irreducible non-torus plane sextic;    Fundamental group;    Alexander-equivalent Zariski pair;   

DOI  :  10.2996/kmj/1257948887

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(16)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.

【 授权许可】

Unknown