Tohoku Mathematical Journal

Weak geometric structures on submanifolds of affine spaces

Barbara Opozda

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Abstract

A few affine invariant structures depending only on the second fundamental form relative to arbitrary transversal bundles on submanifolds of the standard affine spaces are introduced. A notion of “local strong convexity” is proposed for arbitrary codimensional submanifolds. In the case of $n$-dimensional submanifolds of $2n$-dimensional real affine spaces, complex structures on the ambient spaces are used as a tool for studying real affine invariants.

Article information

Source
Tohoku Math. J. (2), Volume 60, Number 3 (2008), 383-401.

Dates
First available in Project Euclid: 3 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1223057735

Digital Object Identifier
doi:10.2748/tmj/1223057735

Mathematical Reviews number (MathSciNet)
MR2453730

Zentralblatt MATH identifier
1181.53010

Subjects
Primary: 53B25: Local submanifolds [See also 53C40]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
Affine invariant affine connection conformal structure ellipse of curvature

Citation

Opozda, Barbara. Weak geometric structures on submanifolds of affine spaces. Tohoku Math. J. (2) 60 (2008), no. 3, 383--401. doi:10.2748/tmj/1223057735. https://projecteuclid.org/euclid.tmj/1223057735


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References

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  • B. Opozda, Flat affine Lagrangian surfaces in $\boldsymbolC^2$, preprint.