A note on homotopy complex surfaces with negative tangent bundles

Bun Wong

Vol. 151 (1991), No. 2, 369–377

DOI: 10.2140/pjm.1991.151.369

Abstract

We propose some problems concerning a weak rigidity phenomenon on compact complex manifolds with negative tangent bundles. Some observations have been made in the two dimensional case as an easy consequence of classification theory, and Yau’s theorem on the rigidity of ℂP₂. We point out that among the class of complex surfaces of general type with c₁² −c₂ > 0 the cotangent dimension is a homotopy invariant possibly except in the case of S² × S².

Mathematical Subject Classification 2000

Primary: 32J15

Secondary: 32J27, 53C55, 57R55

Milestones

Received: 7 July 1990

Published: 1 December 1991