
Some remarks on the geometry of austere manifolds
Publication
, Journal Article
Bryant, RL
Published in: Boletim da Sociedade Brasileira de Matemática
September 1, 1991
We prove several structure theorems about the special class of minimal submanifolds which Harvey and Lawson have called "austere" and which arose in connection with their foundational work on calibrations. The condition of austerity is a pontwise condition on the second fundamental form and essentially requires that the non-zero eigenvalues of the second fundamental form in any normal direction at any point occur in oppositely signed pairs. We solve the pointwise problem of describing the set of austere second fundamental forms in dimension at most four and the local problem of describing the austere three-folds in Euclidean space in all dimensions. © 1991 Sociedade Brasileira de Matemática.
Duke Scholars
Published In
Boletim da Sociedade Brasileira de Matemática
DOI
EISSN
1678-7714
ISSN
0100-3569
Publication Date
September 1, 1991
Volume
21
Issue
2
Start / End Page
133 / 157
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Bryant, R. L. (1991). Some remarks on the geometry of austere manifolds. Boletim Da Sociedade Brasileira de Matemática, 21(2), 133–157. https://doi.org/10.1007/BF01237361
Bryant, R. L. “Some remarks on the geometry of austere manifolds.” Boletim Da Sociedade Brasileira de Matemática 21, no. 2 (September 1, 1991): 133–57. https://doi.org/10.1007/BF01237361.
Bryant RL. Some remarks on the geometry of austere manifolds. Boletim da Sociedade Brasileira de Matemática. 1991 Sep 1;21(2):133–57.
Bryant, R. L. “Some remarks on the geometry of austere manifolds.” Boletim Da Sociedade Brasileira de Matemática, vol. 21, no. 2, Sept. 1991, pp. 133–57. Scopus, doi:10.1007/BF01237361.
Bryant RL. Some remarks on the geometry of austere manifolds. Boletim da Sociedade Brasileira de Matemática. 1991 Sep 1;21(2):133–157.

Published In
Boletim da Sociedade Brasileira de Matemática
DOI
EISSN
1678-7714
ISSN
0100-3569
Publication Date
September 1, 1991
Volume
21
Issue
2
Start / End Page
133 / 157
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics