## Tohoku Mathematical Journal

### Weak geometric structures on submanifolds of affine spaces

Barbara Opozda

#### 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

https://projecteuclid.org/euclid.tmj/1223057735

Digital Object Identifier
doi:10.2748/tmj/1223057735

Mathematical Reviews number (MathSciNet)
MR2453730

Zentralblatt MATH identifier
1181.53010

#### 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

#### References

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• B. Opozda, Affine geometry of special real submanifolds of $\boldsymbolC^n$, Geom. Dedicata 121 (2006), 155--166.
• B. Opozda, Flat affine Lagrangian surfaces in $\boldsymbolC^2$, preprint.