Symmetric R-Spaces

Authors : Kadri ASLAN

Pages : 0-0

Doi:10.1501/Commua1_0000000474

View : 13 | Download : 5

Publication Date : 1994-01-01

Article Type : Research Paper

Abstract :Submanifolds with parallel second fundamental form are defincd as extrinsic analogue of locally symmetric manifolds [6, 7]. It follovvs that ali of them are locally invariant under the reflection in the normal space of an arbitrary point. These type of submanifolds are also cailed symmetric submamfolds [7 ]. Examples are symmetric jR-spaces. Submanifolds with pointwise planar normal sections insert ignore into journalissuearticles values(P2-PNS); are introduced in [3, 4, 5 ]. It bas shown tliat spherical submanifolds have P2-PNS property if and only if they must be parellel submanifolds. In [İJ the present author and A. West showed that non-parallel submanifold M has P2-PNS property if and only if It is a hypersurface. In this article we prove that if M is a symmetric R-space then it must be tlıe orbit of the element A such that ad insert ignore into journalissuearticles values(A););^ = ad{ We also show that the imbeddings of the symmetric K-spaces of tlıe form f: M = Kİ Ko —■ P by f insert ignore into journalissuearticles values([fc]); = insert ignore into journalissuearticles values(k); have P2-PNS.
Keywords : Symmetric, R Spaces, parallel second fundamental