Generic linear perturbations
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- by Shunsuke Ichiki PDF
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Abstract:
In his celebrated paper Generic projections, John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an improvement of Mather’s result is stated. Namely, we show that almost all linear perturbations of a smooth mapping from a submanifold of $\mathbb {R}^m$ into $\mathbb {R}^\ell$ yield a transverse mapping with respect to a given modular submanifold. Moreover, applications of this result are given.References
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Additional Information
- Shunsuke Ichiki
- Affiliation: Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama 240-8501, Japan
- MR Author ID: 1015474
- Email: ichiki-shunsuke-jb@ynu.jp
- Received by editor(s): June 23, 2017
- Received by editor(s) in revised form: January 12, 2018
- Published electronically: August 8, 2018
- Additional Notes: The author is a Research Fellow PD of Japan Society for the Promotion of Science. The author is supported by JSPS KAKENHI Grant Number 16J06911.
- Communicated by: Ken Ono
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4981-4991
- MSC (2010): Primary 57R45, 58K25, 57R40
- DOI: https://doi.org/10.1090/proc/14094
- MathSciNet review: 3856163