Semistability of restricted tangent bundles and a question of I. Biswas

TL;DR

This paper proves that complex projective manifolds with semistable tangent bundle pullbacks from all Riemann surfaces are either curves or quotients of abelian varieties, confirming a conjecture of I. Biswas.

Contribution

It establishes a classification of such manifolds, showing they are either curves or finite étale quotients of abelian varieties, thus resolving Biswas's conjecture.

Findings

Manifolds with semistable tangent bundle pullbacks are classified as curves or quotients of abelian varieties.

The conjecture of I. Biswas is confirmed for this class of manifolds.

The result links the semistability condition to the geometric structure of the manifold.

Abstract

Let M be a complex projective manifold with the property that for any compact Riemann surface C and holomorphic map f: C -> M the pullback of the tangent bundle of M is semistable. We prove that in this case M is a curve or a finite etale quotient of an abelian variety answering a conjecture of I. Biswas.