A new look at adapted complex structures

TL;DR

This paper introduces a novel family of adapted complex structures on the geodesic manifold of a closed real analytic Riemannian manifold, providing new insights into its geometric properties.

Contribution

It constructs and analyzes a one-parameter family of adapted complex structures on the geodesic manifold, advancing understanding of complex structures in Riemannian geometry.

Findings

Construction of a continuous family of complex structures

Analysis of geometric properties of these structures

Potential applications to geometric analysis

Abstract

Given a closed real analytic Riemannian manifold, we construct and study a one parameter family of adapted complex structures on the manifold of its geodesics.