About: Barrett O'Neill

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Barrett O'Neill (1924– 16 June 2011) was an American mathematician. He is known for contributions to differential geometry, including two widely-used textbooks on its foundational theory. He was the author of eighteen research articles, the last of which was published in 1973. He received his Ph.D. in mathematics in 1951 from the Massachusetts Institute of Technology. His doctoral advisor was Witold Hurewicz. His dissertation thesis was titled Some Fixed Point Theorems He has worked as a professor of mathematics at UCLA, where he supervised the PhDs of eight doctoral students.

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rdfs:label	Barrett O'Neill (en)
rdfs:comment	Barrett O'Neill (1924– 16 June 2011) was an American mathematician. He is known for contributions to differential geometry, including two widely-used textbooks on its foundational theory. He was the author of eighteen research articles, the last of which was published in 1973. He received his Ph.D. in mathematics in 1951 from the Massachusetts Institute of Technology. His doctoral advisor was Witold Hurewicz. His dissertation thesis was titled Some Fixed Point Theorems He has worked as a professor of mathematics at UCLA, where he supervised the PhDs of eight doctoral students. (en)
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dcterms:subject	1924 births 2011 deaths 20th-century American mathematicians 21st-century American mathematicians Massachusetts Institute of Technology School of Science alumni
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Link from a Wikipage to another Wikipage	Richard L. Bishop 1924 births 2011 deaths Massachusetts Institute of Technology 20th-century American mathematicians 21st-century American mathematicians UCLA Riemannian geometry Riemannian submersion Massachusetts Institute of Technology School of Science alumni Differential geometry Witold Hurewicz Warped geometry Sectional curvature
Link from a Wikipage to an external page	https://scholar.google.com/scholar%3Fhl=en&q=Barrett+O%27Neill&btnG=&as_sdt=1%2C6&as_sdtp= https://www.math.ucla.edu/news/memoriam-barrett-oneill-professor-mathematics-emeritus-1924-%E2%80%93-2011 https://mathscinet.ams.org/mrlookup
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has abstract	Barrett O'Neill (1924– 16 June 2011) was an American mathematician. He is known for contributions to differential geometry, including two widely-used textbooks on its foundational theory. He was the author of eighteen research articles, the last of which was published in 1973. He received his Ph.D. in mathematics in 1951 from the Massachusetts Institute of Technology. His doctoral advisor was Witold Hurewicz. His dissertation thesis was titled Some Fixed Point Theorems He has worked as a professor of mathematics at UCLA, where he supervised the PhDs of eight doctoral students. 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 formula" refers to the relation between the sectional curvatures. O'Neill's calculations simplified earlier work by other authors, and have become standard textbook material. With Richard Bishop, he applied his submersion calculations to the geometry of warped products, in addition to studying the fundamental role of convex functions and convex sets in Riemannian geometry, and for the geometry of negative sectional curvature in particular. 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". (en)
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is Link from a Wikipage to another Wikipage of	Richard L. Bishop Jacobi field Riemannian submersion Witold Hurewicz
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