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島根大学総合理工学部紀要. シリーズB Volume 40
published_at 2007-03
Submanifold theory from the viewpoint of circles
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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.
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.
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