×

On infinitesimal holomorphically projective transformations in Tachibana spaces. (English) Zbl 1054.53068

An almost Hermitian manifold \({\mathcal M}= ({\mathcal M}, J, {\mathcal G})\) satisfying the condition \(\nabla_j {\mathcal J}_{ik}+ \nabla_i {\mathcal J}_{jk}= 0\) is called an almost Tachibana space (called also nearly Kähler manifold) and further, if the almost complex structure \({\mathcal J}\) is integrable, \({\mathcal M}\) is called a Tachibana-space (called also Kähler manifold). In the present article, the authors discuss with infinitesimal holomorphically projective transformations in Kähler manifolds and show some results. However, all the results stated in the present article are included in the book of K. Yano [Differential geometry on complex and almost complex spaces (Pergamon Press, Oxford) (1965; Zbl 0127.12405)]. So, the authors essentially do not obtain any original results.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)

Citations:

Zbl 0127.12405
PDFBibTeX XMLCite