Back to Search
Start Over
Fine structure of the space of spherical minimal immersions.
- Source :
-
Transactions of the American Mathematical Society . Jun1996, Vol. 348 Issue 6, p2441-2463. 23p. - Publication Year :
- 1996
-
Abstract
- The space of congruence classes of full spherical minimal immersions $f:S^m\to S^n$ of a given source dimension $m$ and algebraic degree $p$ is a compact convex body $\mathcal{M}_m^p$ in a representation space $\mathcal{F}_m^p$ of the special orthogonal group $SO(m+1)$. In Ann. of Math. {\bf 93} (1971), 43--62 DoCarmo and Wallach gave a lower bound for $\mathcal{F}_m^p$ and conjectured that the estimate was sharp. Toth resolved this ``exact dimension conjecture'' positively so that all irreducible components of $\mathcal{F}_m^p$ became known. The purpose of the present paper is to characterize each irreducible component $V$ of $\mathcal{F}_m^p$ in terms of the spherical minimal immersions represented by the slice $V\cap \mathcal{M}_m^p$. Using this geometric insight, the recent examples of DeTurck and Ziller are located within $\mathcal{M}_m^p$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GEOMETRIC congruences
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 348
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 9494828
- Full Text :
- https://doi.org/10.1090/S0002-9947-96-01588-7