6533b851fe1ef96bd12a95d4

RESEARCH PRODUCT

A historical account on characterizations ofC1-manifolds in Euclidean spaces by tangent cones

Sebastiano Nicolussi GoloFrancesco Bigolin

subject

Tangent bundlePure mathematicsApplied MathematicsMathematical analysisTangent coneTangentManifoldVertical tangentTangent spacePushforward (differential)Mathematics::Differential GeometryTangent vectorAnalysisMathematics

description

Abstract A historical account on characterizations of C 1 -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 [1] .

yearjournalcountryeditionlanguage
2014-04-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2013.10.035