# Colloquium abstracts

**Ananya Chaturvedi**

TIFR, Mumbai

November 22, 2018

**On Holomorphic Sectional Curvature and Fibration**: A fibration, loosely speaking, is generalization of the concept of a fiber bundle. For a given fibration, we can talk about its two ?directions?: base and fibers. Suppose we are given Hermitian metrics on the base and fibers of a holomorphic fibration such that the holomorphic sectional curvatures have same signs on the base and fibers. Then, we show that the given metrics in the two ?directions? can be used to construct a warped product metric on the total space such that this metric has the same sign of the holomorphic sectional curvature on the total space as that of the given metrics on the base and fibers. The case of negative holomorphic sectional curvature was proved by Cheung in 1989. In this talk, we shall focus on the positive holomorphic sectional curvature case.