On the Total Curvature and Betti Numbers of Complex Projective Manifolds

TL;DR

This paper establishes a new inequality linking the total curvature and Betti numbers of complex projective manifolds, extending classical theorems and characterizing minimal curvature cases.

Contribution

It introduces a novel inequality connecting total curvature and Betti numbers for complex projective manifolds, expanding classical geometric results.

Findings

Proved an inequality relating Betti numbers and total curvature.

Characterized manifolds with minimal total curvature.

Extended classical theorems of Chern and Lashof.

Abstract

We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.