Schur's theorem of antiholomorphic type for quasi-K\"ahlerian manifolds

TL;DR

This paper proves that in higher-dimensional quasi-K"ahler manifolds with pointwise constant antiholomorphic sectional curvature, key curvature invariants such as scalar and $*$-scalar curvatures are necessarily constant.

Contribution

It establishes a Schur-type theorem for quasi-K"ahler manifolds of dimension at least 6 with antiholomorphic sectional curvature.

Findings

Antiholomorphic sectional curvature $ u$ is constant under given conditions.

Scalar curvature and $*$-scalar curvature are constant in these manifolds.

Results extend classical Schur's theorem to a broader geometric setting.

Abstract

It is proved, that if a quasi-K\"ahler manifold $M$ of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature $\nu$, then $\nu$, the scalar curvature and the $*$-scalar curvature of $M$ are constants.