Constancy of $\phi-$holomorphic scetional curvature in generalized $g.f.f-$manifolds

TL;DR

This paper generalizes Tanno's algebraic characterization of constant holomorphic sectional curvature from almost Hermitian and Sasakian manifolds to the broader class of generalized g.f.f.-manifolds.

Contribution

It extends the algebraic criteria for constant holomorphic sectional curvature to generalized g.f.f.-manifolds, broadening the scope of geometric analysis.

Findings

Characterization of constant holomorphic sectional curvature in generalized g.f.f.-manifolds

Extension of Tanno's results to a wider class of manifolds

Potential implications for geometric structures in complex and contact geometry

Abstract

Tanno [6] provided an algebraic characterization in an almost Hermitian manifold to reduce to a space of constant holomorphic sectional curvature, which he later extended for the Sasakian manifolds as well. In this present paper, we generalize the same characterization in generalized $g.f.f-$manifolds.