Tohoku Mathematical Journal

Weak geometric structures on submanifolds of affine spaces

Barbara Opozda

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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

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

First available in Project Euclid: 3 October 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Affine invariant affine connection conformal structure ellipse of curvature


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.

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