Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 67-78 (1999)

Immersions into the Hyperbolic Space Invariant by Reflections

Antonella Carfagna D'Andrea, Sergio Console

Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universita di Roma "La Sapienza", via Scarpa, 8; I-00185 Roma e-mail: carfagna@dmmm.uniroma1.it

Dipartimento di Matematica, Universita di Torino, via Carlo Alberto, 10; I-10123 Torino e-mail: console@dm.unito.it

Abstract: In this paper we prove that a nicely curved full submanifold of the hyperbolic space with parallel higher fundamental forms is 2-symmetric. This allows to give examples of 2-symmetric submanifolds of the hyperbolic space. Moreover we prove a splitting theorem for 2-symmetric submanifolds of a space of constant curvature.

Classification (MSC91): 53C42; 53C35

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