島根大学総合理工学研究科
ISSN:1342-7121
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Use this link to cite this item : https://ir.lib.shimane-u.ac.jp/6171
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 40
2007-03 発行
Submanifold theory from the viewpoint of circles
Maeda, Sadahiro
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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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