In her most widely-known work, published in 1982, Michelsohn introduced the notion of a balanced metric on a complex manifold. These are hermitian metrics for which the penultimate power of the associated Kähler form is closed, i.e.
in which ω is the Kähler form and n is the complex dimension. It is trivial to see that every Kähler metric is a balanced metric. As for Kähler metrics, the above definition of a balanced metric automatically places cohomological restrictions on the underlying manifold; by Stokes' theorem, every codimension-one complex subvariety is homologically nontrivial. For instance, the Calabi-Eckmann complex manifolds do not support any balanced metrics. Michelsohn also recast the definition of a balanced metric in terms of the torsion tensor and in terms of the Dirac operator. In parallel to a work of Reese Harvey and Blaine Lawson's on Kähler metrics, Michelsohn obtained a full characterization, in terms of the cohomological theory of currents, of which complex manifolds admit balanced metrics.
Marie-Louise Michelsohn setting the W75 world record in the steeplechase
Michelsohn is also an accomplished middle and long-distance runner. She holds five masters athletics world records including through three age divisions of the 2000 metres steeplechase which she has held since 2002.[1] In addition to the world records, she holds 6 more outdoor American records and 10 indoor American records, running the table of all official indoor distances 800 metres and above in both the W65 and W70 divisions.[2]
Notable publicationsedit
Michelsohn, M. L. (1982). "On the existence of special metrics in complex geometry". Acta Mathematica. 149: 261–295. doi:10.1007/BF02392356. MR 0688351. Zbl 0531.53053.
Notable Women in Mathematics, a Biographical Dictionary, edited by Charlene Morrow and Teri Perl, Greenwood Press, 1998. p 142–147.
January 01, 1970
marie, louise, michelsohn, born, october, 1941, professor, mathematics, state, university, york, stony, brook, michelsohn, 1982, contents, education, mathematical, work, masters, athletics, notable, publications, notes, referenceseducation, editmichelsohn, att. Marie Louise Michelsohn born October 8 1941 is a professor of mathematics at State University of New York at Stony Brook Michelsohn in 1982 Contents 1 Education 2 Mathematical work 3 Masters athletics 4 Notable publications 5 Notes 6 ReferencesEducation editMichelsohn attended the Bronx High School of Science She attended the University of Chicago for her undergraduate and graduate studies including her PhD She spent a year as a visiting professor at University of California at San Diego She spent a year l Institut des Hautes Etudes Scientifiques outside of Paris France She then joined the faculty of State University of New York at Stony Brook Mathematical work editMichelsohn s PhD was in the field of topology As of 2020 she has published twenty articles on topics including complex geometry spin manifolds and the Dirac operator and the theory of algebraic cycles Half of her work has been in collaboration with Blaine Lawson With Lawson she wrote a textbook on spin geometry which has become the standard reference for the field In her most widely known work published in 1982 Michelsohn introduced the notion of a balanced metric on a complex manifold These are hermitian metrics for which the penultimate power of the associated Kahler form is closed i e d w w n 1 times 0 displaystyle d underbrace omega wedge cdots wedge omega n 1 text times 0 nbsp in which w is the Kahler form and n is the complex dimension It is trivial to see that every Kahler metric is a balanced metric As for Kahler metrics the above definition of a balanced metric automatically places cohomological restrictions on the underlying manifold by Stokes theorem every codimension one complex subvariety is homologically nontrivial For instance the Calabi Eckmann complex manifolds do not support any balanced metrics Michelsohn also recast the definition of a balanced metric in terms of the torsion tensor and in terms of the Dirac operator In parallel to a work of Reese Harvey and Blaine Lawson s on Kahler metrics Michelsohn obtained a full characterization in terms of the cohomological theory of currents of which complex manifolds admit balanced metrics Balanced metrics are in part of interest due to their role in the Strominger system arising from string theory Masters athletics edit nbsp Marie Louise Michelsohn setting the W75 world record in the steeplechase Michelsohn is also an accomplished middle and long distance runner She holds five masters athletics world records including through three age divisions of the 2000 metres steeplechase which she has held since 2002 1 In addition to the world records she holds 6 more outdoor American records and 10 indoor American records running the table of all official indoor distances 800 metres and above in both the W65 and W70 divisions 2 Notable publications editMichelsohn M L 1982 On the existence of special metrics in complex geometry Acta Mathematica 149 261 295 doi 10 1007 BF02392356 MR 0688351 Zbl 0531 53053 Lawson H Blaine Jr Michelsohn Marie Louise 1989 Spin geometry Princeton Mathematical Series Vol 38 Princeton NJ Princeton University Press ISBN 0 691 08542 0 MR 1031992 Zbl 0688 57001 Notes edit Records Outdoor Women Archived from the original on 2012 01 11 Retrieved 2012 01 11 USATF Statistics Records References editNotable Women in Mathematics a Biographical Dictionary edited by Charlene Morrow and Teri Perl Greenwood Press 1998 p 142 147 Retrieved from https en wikipedia org w index php title Marie Louise Michelsohn amp oldid 1215194107, wikipedia, wiki, book, books, library,
