Homogeneous Submanifolds of Codimension Two |
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Authors: | Helvecio Pereira De Castro Maria Helena Noronha |
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Affiliation: | (1) Departamento de Matemática, Universidade Federal de Goiás, CP 131, 74.001-970 Goiania, GO, Brasil;(2) Department of Mathematics, California State University Northridge, Northridge, CA 91330-8313, USA |
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Abstract: | We study codimension 2 homogeneous submanifolds of Euclidean space for which the index of minimum relative nullity is small. We prove that if minxMf(x)n-5, where (x) denotes the nullity of the second fundamental form of the immersion f at the point x, then the manifold Mn is either isometric to a sphere or to a product of two spheres S2×Sn–2 or covered by the Riemannian product Sn–1 ×R. As a consequence, we obtain a classification of compact codimension 2 homogeneous submanifolds of dimension at least 5. |
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Keywords: | Isometry relative nullity rigid immersions. |
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