A historical account on characterizations of -manifolds in Euclidean spaces by tangent cones
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- 作者：Francesco Bigolin ; Sebastiano Nicolussi Golo
- 关键词：Tangent cones ; Peano tangent cones ; Bouligand tangent cones ; Severi tangent cones ; Clarke tangent cone ; Paratangency tangency and differentiability ; C1C1-manifolds
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：1 April, 2014
- 年：2014
- 卷：412
- 期：1
- 页码：63-76
- 全文大小：320 K
文摘
A historical account on characterizations of -manifolds in Euclidean spaces by tangent cones is provided. Old characterizations of smooth manifold (by tangent cones), due to Valiron (1926, 1927) and Severi (1929, 1934) are recovered; modern characterizations, due to Gluck (1966, 1968) and Tierno (1997) are restated. All these results are consequences of the Four-cones coincidence theorem due to .