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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

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MLA
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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.
Journal cover image

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