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dc.contributor.advisor Harvey, F. Reese
dc.creatorEarles, Christopher Michael
dc.date.accessioned 2009-06-04T06:49:13Z
dc.date.available 2009-06-04T06:49:13Z
dc.date.issued 2003
dc.identifier.urihttps://hdl.handle.net/1911/18522
dc.description.abstract We present the theory of atomic sections developed by Harvey and Lawson, and we use it to study the repeated eigenvalue currents of symmetric bilinear forms. The main example is the classical theorem of surface theory which equates the total index of the umbilic points to the Euler characteristic of a compact surface in R3 . We derive this from the Harvey-Lawson viewpoint and extend it to surfaces with boundary. To develop analogous results for hypersurfaces in R2n+1 , we first prove a Splitting Principle for the differential characters of an oriented, even rank, real vector bundle and use it to compute the Euler character of the bundle of traceless symmetric bilinear forms. Finally, we show that partial umbilics of even type are boundaries with the single exception of the partial umbilics of type (2,...,2) (with n twos), which represent a multiple of the Euler class.
dc.format.extent 143 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title Partial umbilics of hypersurfaces and repeated eigenvalue currents
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Earles, Christopher Michael. "Partial umbilics of hypersurfaces and repeated eigenvalue currents." (2003) Diss., Rice University. https://hdl.handle.net/1911/18522.


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