Contact Riemannian manifolds satisfying C(^)S=0 AND 4e(k, n)-nullity distribution

Authors : Cengizhan MURATHAN

Pages : 0-0

Doi:10.1501/Commua1_0000000376

View : 6 | Download : 5

Publication Date : 2000-01-01

Article Type : Research Paper

Abstract :Let ,cp,Ç,n,g); be a contact Riemannian manifold of dimension 2n+l>3. Tanno [6] proved that insert ignore into journalissuearticles values(M^’,cp,§,r|,g); is an Einstein manifold and Ç belongs to the k-nullity distribution, then M is a Sasakian manifold and Perrone [4] proved that if M is a contact Riemannian manifold with Rinsert ignore into journalissuearticles values(X,Ç);S=0 and Ç belongs to the k-nulhty distribution, where ke R, then M is either an Einstein-Sasakian manifold or the produet E`^’insert ignore into journalissuearticles values(0);xS`insert ignore into journalissuearticles values(4);. Papantoniou [1] generahzing this result proved that if M is a contact Riemannian manifold with Rinsert ignore into journalissuearticles values(X,Ç);S=0 and § belongs to the insert ignore into journalissuearticles values(k,ıx);-nullity distribution, where insert ignore into journalissuearticles values(k,);j.);e R^, then M is local isometric to E“^`insert ignore into journalissuearticles values(0);xS`insert ignore into journalissuearticles values(4); or an Einstein-Sasakian manifold or, an r|-Einstein manifold.The purpose of this paper is to classify the contact- manifolds satisfying Cinsert ignore into journalissuearticles values(X,Ç);S=0 under the condition that characteristic vector field belongs to the insert ignore into journalissuearticles values(k,p,);-nullity distribution.
Keywords : Contact Riemannian, manifolds satisfying, nullity distribution