Displaying similar documents to “Transversally symmetric immersions”

Locally symmetric immersions

José Carmelo González-Dávila, Lieven Vanhecke (1999)

Czechoslovak Mathematical Journal

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We use reflections with respect to submanifolds and related geometric results to develop, inspired by the work of Ferus and other authors, in a unified way a local theory of extrinsic symmetric immersions and submanifolds in a general analytic Riemannian manifold and in locally symmetric spaces. In particular we treat the case of real and complex space forms and study additional relations with holomorphic and symplectic reflections when the ambient space is almost Hermitian. The global...

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...