Tohoku Mathematical Journal
2008
September
SECOND SERIES VOL. 60, NO. 3

Tohoku Math. J.
60 (2008), 383-401

Title WEAK GEOMETRIC STRUCTURES ON SUBMANIFOLDS OF AFFINE SPACES

Author Barbara Opozda

(Received September 11, 2007, revised February 26, 2008)
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.

2000 Mathematics Subject Classification. Primary 53B25; Secondary 53C15.
Key words and phrases. Affine invariant, affine connection, conformal structure, ellipse of curvature.

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