島根大学総合理工学部紀要.シリーズB

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島根大学総合理工学部紀要.シリーズB 40
2007-03 発行

Submanifold theory from the viewpoint of circles

前田 定廣
ファイル
内容記述(抄録等)
We study submanifolds by using the notion of circles in Riemannian
geometry. This expository paper consists of two parts. One is to improve Nomizu and Yano’s result ([11]) which characterizes extrinsic spheres in a Riemannian manifold. The other is to characterize totally geodesic immersions and some parallel immersions in terms of Frenet curves of proper order 2 (which are generalizations of circles) on submanifolds.