Abstract
We prove that if the f-sectional curvature at any point of a ( 2 n + s ) -dimensional metric f-contact manifold satisfying the ( κ , μ ) nullity condition with n > 1 is independent of the f-section at the point, then it is constant on the manifold. Moreover, we also prove that a non-normal metric f-contact manifold satisfying the ( κ , μ ) nullity condition is of constant f-sectional curvature if and only if μ = κ + 1 and we give an explicit expression for the curvature tensor field in such a case. Finally, we present some examples.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference25 articles.
1. On a structure defined by a tensor field f of type (1,1) satisfying f3 + f = 0;Yano;Tensor,1963
2. The curvature tensor fields on f-manifolds with complemented frames;Cabrerizo;An. Ştiinţ Univ. Al. I. Cuza Iaşi Secţ. I A Mat.,1990
3. Geometry of manifolds with structural group ${\cal U}(n)\times {\cal O}(s)$
4. On normal globally framed $f$-manifolds