Displaying similar documents to “An Arzela-Ascoli theorem for immersed submanifolds”

Semiparallel isometric immersions of 3-dimensional semisymmetric Riemannian manifolds

Ülo Lumiste (2003)

Czechoslovak Mathematical Journal

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A Riemannian manifold is said to be semisymmetric if R ( X , Y ) · R = 0 . A submanifold of Euclidean space which satisfies R ¯ ( X , Y ) · h = 0 is called semiparallel. It is known that semiparallel submanifolds are intrinsically semisymmetric. But can every semisymmetric manifold be immersed isometrically as a semiparallel submanifold? This problem has been solved up to now only for the dimension 2, when the answer is affirmative for the positive Gaussian curvature. Among semisymmetric manifolds a special role is played...

Reflections with respect to submanifolds in contact geometry

P. Bueken, Lieven Vanhecke (1993)

Archivum Mathematicum

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We study to what extent some structure-preserving properties of the geodesic reflection with respect to a submanifold of an almost contact manifold influence the geometry of the submanifold and of the ambient space.