Barrett O'Neill

[1] He is known for contributions to differential geometry, including two widely-used textbooks on its foundational theory.

His dissertation thesis was titled Some Fixed Point Theorems[3] He has worked as a professor of mathematics at UCLA, where he supervised the PhDs of eight doctoral students.

[3] He made a foundational contribution to the theory of Riemannian submersions, showing how geometric quantities on the total space and on the base are related to one another.

O'Neill's calculations simplified earlier work by other authors, and have become standard textbook material.

An article with his former Ph.D. student Patrick Eberlein made a number of further contributions to the Riemannian geometry of negative curvature, including the notion of the "boundary at infinity".